Linear Pelton turbine

ABSTRACT

Systems and methods related to linear turbine systems are presented. Each embodiment described herein may be designed as a single-stage, linear, impulse turbine system. In an embodiment, a linear turbine includes a first shaft extending along a first axis; a second shaft extending along a second axis, the second axis being separated from and substantially parallel to the first axis; a first plurality of buckets to travel a first continuous path around the first shaft and the second shaft along a first plane, the first path including a first substantially linear path segment between the first axis and the second axis; and a nozzle configured to direct a first fluid jet to contact the first plurality of buckets in the first linear path segment.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 62/367,003, filed Jul. 26, 2016, and U.S. ProvisionalPatent Application No. 62/485,694, filed Apr. 14, 2017, both of whichare incorporated herein by reference in their entireties, for allpurposes.

BACKGROUND

Hydroelectric power generation harnesses flowing water—typically using adam or other type of diversion structure—and converts kinetic energy(typically via a turbine) to generate electricity. The power output of aturbine involves the product of vertical head H (the vertical change inelevation the water level) and flow rate Q (the volume of water passinga point in a given amount of time) at a particular site. Head produceswater pressure, and the greater the head, the greater the pressure todrive turbines. More head or higher flow rate translates to more power.

As illustrated in FIG. 68, these factors largely determine the type ofturbine to be used at a particular site. Other non-limiting factorsinclude how deep the turbine must be installed at a project relative tothe water level downstream of the turbine (tailwater), efficiency, andcost.

Although hydraulic turbomachinery has seen widespread use for over acentury, most conventional equipment is optimally suited for high headapplication, where environmental impacts may be severe. Most of theremaining hydroelectric energy generating potential that can bedeveloped with relatively low environmental impact is located at siteswith less than 10 meters of head.

Turbines historically finding application at low head have includedwaterwheels, Archimedean screws, and variations of propeller typeturbines. Waterwheels and Archimedean screw turbines are progressivecavity devices, in which a bucket delivers a quantity of water from anupper elevation to a lower elevation, and the water quanta moves at thesame speed as the bucket. Consequentially, these types of devicesoperate slowly and must be very large in order to pass large quantitiesof water. Propeller turbines and their derivatives, such as Kaplanturbines, can pass large quantities of water moving at high velocityacross the turbine blades, but they may require large draft tubes torecover kinetic energy remaining in the fluid after leaving the turbineblades, and the units may need to be installed at a relatively lowelevation with respect to the water level downstream of the turbine, toprevent operating problems such as cavitation. Consequentially,conventional turbines designed to produce power from low heads havetypically been highly expensive, with extensive civil works necessitatedby the operation requirements of the turbines.

Accordingly, there remains a need for a simple, highly efficient impulseturbine that is capable of operating high flow and a low head,especially at head of 10 meters or less. In addition, the environmentalimpact of a hydropower installation must also be taken intoconsideration.

BRIEF SUMMARY

Systems and methods related to linear turbine systems are presented.Each embodiment described herein may be designed as a single-stage,linear, impulse turbine system. In an embodiment, a linear turbineincludes a first shaft extending along a first axis; a second shaftextending along a second axis, the second axis being separated from andsubstantially parallel to the first axis; a first plurality of bucketsto travel a first continuous path around the first shaft and the secondshaft along a first plane, the first path including a firstsubstantially linear path segment between the first axis and the secondaxis; and a nozzle configured to direct a first fluid jet to contact thefirst plurality of buckets in the first linear path segment. The linearturbine may also include a second plurality of buckets to travel asecond continuous path around the first shaft and the second shaft alonga second plane, the second plane being substantially parallel to thefirst plane, the second path including a second substantially linearpath segment between the first axis and the second axis, wherein thenozzle is configured to direct a second fluid jet to contact the secondplurality of buckets in the second linear path segment. The nozzle ofthe linear turbine may be positioned between the first plane and thesecond plane and configured to direct the first fluid jet and secondfluid jet outward to contact the first and second plurality of buckets.

In the embodiment, the nozzle may direct the first fluid jet to contactthe first plurality of buckets at a non-zero inlet angle. In theembodiment, the first plurality of buckets and/or the second pluralityof buckets are mounted to a powertrain, the powertrain having a driveshaft coupled to the first axis, the drive shaft being configured todrive an electric generator. In the embodiment, the first path mayfurther include a second substantially linear path segment, a firstsubstantially arc-shaped segment, and a second substantially arc-shapedsegment. The linear turbine may be configured such that the first fluidjet does not contact the first plurality of buckets in the secondsubstantially linear path segment. The nozzle may be a free-jet nozzle.The nozzle may also be positioned below a horizontal plane extendingbetween the first axis and the second axis. The nozzle may be furtherconfigured to substantially distribute the first fluid jet at an angleto the first substantially linear path segment, the angle having a rangefrom approximately 0° to approximately 50°. The nozzle may be furtherconfigured to substantially distribute the first fluid jet at an angleto the first substantially linear path segment, the angle having a rangefrom approximately 10° to approximately 40°. The nozzle may be furtherconfigured to substantially distribute the first fluid jet at an angleto the first substantially linear path segment, the angle having a rangefrom approximately 15° to approximately 35°.

In another embodiment, a single-stage linear turbine includes a firstshaft extending along a first horizontal axis; a second shaft extendingalong a second horizontal axis, the second axis being separated from andsubstantially parallel to the first horizontal axis; a bucket to travela first continuous path around the first shaft and the second shaftalong a first plane, the first path including a first substantiallylinear path segment between the first axis and the second axis, a firstsubstantially arc-shaped segment around the second axis, a secondsubstantially linear path segment between the second axis and the firstaxis, and a second substantially arc-shaped segment around the firstaxis; and a nozzle configured to direct a fluid jet to contact thebucket in the first substantially linear path segment. The linearturbine may be configured such that the fluid jet does not contact thebucket in the second substantially linear path segment. The secondsubstantially linear path segment may be positioned above the firstsubstantially linear path segment. The linear turbine may furtherinclude a turbine blade, the bucket being connected to an end of theturbine blade (such as a at a crossbeam). The linear turbine may alsoinclude a moving structure with the turbine blade being connected to themoving structure. In some embodiments, the turbine blade is connected tothe moving structure at its mid-span such that the end of the turbineblade is cantilevered. The moving structure may, for example, be a belt.In an embodiment, the nozzle is positioned below a horizontal planeextending between the first axis and the second axis. The nozzle maydirect the fluid jet outward to contact the bucket. A speed of the fluidjet is greater than a speed of the bucket.

In an embodiment, a nozzle manifold for a linear turbine includes aninlet portion for receiving a volume of fluid, the inlet portion havinga cross-section; a first outlet portion terminating in a firstsubstantially rectilinear opening to provide a first rectilinear jet offluid to the linear turbine; a second outlet portion terminating in asecond substantially rectilinear opening to provide a second rectilinearjet of fluid to the linear turbine; and a bifurcation positioned betweenthe inlet portion and the first and second outlet portions to divide thevolume of fluid into the first outlet portion and the second outletportion. In one embodiment, a distance between the inlet portion and thebifurcation is a range from approximately 0.02 to approximately 2.5times the hydraulic diameter of the nozzle at the inlet cross-section.In one embodiment, a distance between the inlet portion and thebifurcation is a range from approximately 0.03 to approximately 0.1times the hydraulic diameter of the nozzle at the inlet cross-section.The first rectilinear jet of fluid may be configured to exit the firstsubstantially rectilinear opening and enter air as a free jet. In anembodiment, the cross-section of the inlet portion is substantiallyv-shaped. Also, a proximal edge of the inlet portion may beapproximately coincident with the bifurcation.

In addition, the first and second outlet portions may be substantiallysymmetrical. In some embodiments, the first outlet portion directs thefirst rectilinear jet of fluid at an angle with respect to a plane thatextends along the first substantially rectilinear opening, wherein theangle has a range from approximately 0° to approximately 40°. In otherembodiments, the angle has a range from approximately 25° toapproximately 35°. A velocity of the first rectilinear jet of fluid maybe approximately equal to a velocity of the second rectilinear jet offluid. In an embodiment, the first substantially rectilinear openingextends along a first plane and the second substantially rectilinearopening extends along a second plane such that the first plane and thesecond plane are substantially parallel. In other embodiments, the firstsubstantially rectilinear opening extends along a first plane, the firstplane having an angle in a range from approximately −5° to approximately25° with respect to horizontal, more preferably from approximately −5°to approximately 15°.

In an embodiment, the linear turbine may include a first closuremechanism to control an area of the first substantially rectilinearopening. The first closure mechanism may be, for example, a slide gatethat moves from a position adjacent a proximal portion of the firstsubstantially rectilinear opening toward a distal portion of the firstsubstantially rectilinear opening to reduce the area of the firstsubstantially rectilinear opening. A second closure mechanism may alsobe used to control an area of the second substantially rectilinearopening. Like the first closure mechanism, the second closure mechanismmay be, for example, a slide gate that moves from a position adjacent aproximal portion of the second substantially rectilinear opening towarda distal portion of the second substantially rectilinear opening toreduce the area of the second substantially rectilinear opening. Anactuator and linkage may be used to simultaneously move the firstclosure mechanism and the second closure mechanism. Alternatively, thefirst closure mechanism may include rotatable wicket gates positionedadjacent the first substantially rectilinear opening. In either case,the first closure mechanism may include an elastomeric seal and a sealretainer, the seal retainer having an edge such that the firstrectilinear jet of fluid separates cleanly from the seal retainer.

In an embodiment, a linear turbine system includes a linear turbine; anda nozzle configured to provide a fluid jet to the turbine. The nozzlemay include an inlet portion for receiving a volume of fluid, the inletportion having a cross-section; a first outlet portion terminating in afirst substantially rectilinear opening to direct a first rectilinearjet of fluid outward to contact the linear turbine; a second outletportion terminating in a second substantially rectilinear opening todirect a second rectilinear jet of fluid outward to contact the linearturbine; and a bifurcation positioned between the inlet portion and thefirst and second outlet portions to divide the volume of fluid into thefirst outlet portion and the second outlet portion. The first outletportion may direct the first rectilinear jet of fluid into the linearturbine at an angle, for example, in the range from approximately 25° toapproximately 35°.

In an embodiment, a linear turbine system includes a single-stage linearturbine; a free jet nozzle to supply a fluid jet to the turbine; and ahousing configured to isolate the linear turbine and nozzle from anexternal atmosphere. The housing may include a chamber enclosing thelinear turbine and nozzle. The chamber may have an outlet that ishydraulically sealed to an outlet fluid body and a control valveconfigured to control an amount of air in the chamber to maintain adesired elevation of suction head inside the chamber without allowingthe outlet fluid body to contact the turbine. After the fluid jetcontacts the turbine, fluid leaving the turbine exits the housingthrough the outlet. The turbine system may further include a drive shaftdriven by the linear turbine, the drive shaft extending through thehousing and configured to drive an electric generator positionedexterior to the housing. Movement of the fluid jet through an enclosedatmosphere in the chamber may entrain air from the enclosed atmospherein the form of bubbles and momentum of the fluid jet evacuates theentrained bubbles of the enclosed atmosphere from the chamber. Thecontrol valve may be configured to automatically maintain a level of afluid pool below the turbine. In addition, the control valve may beconfigured to automatically maintain a pressure inside the chamber belowthe external atmospheric pressure so as to increase a level of a fluidpool below the turbine.

In an embodiment, the nozzle receives a fluid source at a nozzle inlet,a bottom portion of the nozzle inlet being positioned at a firstelevation, and the nozzle delivers the fluid jet to the turbine at asecond elevation such that the first elevation is lower than the secondelevation. The fluid jet may exit the turbine at a third elevation andthe fluid falls to a fluid pool inside the chamber, a level of the fluidpool being at a fourth elevation such that the third elevation is higherthan the fourth elevation. An exterior fluid surrounding the chamberoutlet outside the chamber may have a level at a fifth elevation suchthat the fourth elevation is higher than the fifth elevation.

In an embodiment, a turbine system as described above may include alinear turbine having a first shaft extending along a first horizontalaxis; a second shaft extending along a second horizontal axis, thesecond axis being separated from and substantially parallel to the firsthorizontal axis; and a first bucket to travel a first continuous patharound the first shaft and the second shaft along a first plane. Thefirst path may include a first substantially linear path segment betweenthe first axis and the second axis, a first substantially arc-shapedsegment around the second axis, a second substantially linear pathsegment between the second axis and the first axis, and a secondsubstantially arc-shaped segment around the first axis. The nozzle maybe configured to direct the fluid jet to contact the first bucket in thefirst substantially linear path segment such that the fluid jet does notcontact the first bucket in the second substantially linear pathsegment. The second substantially linear path segment may positionedabove the first substantially linear path segment.

In an embodiment, a second bucket may travel a second continuous patharound the first shaft and the second shaft along a second plane. Thesecond path may include a first substantially linear path segmentbetween the first axis and the second axis, a first substantiallyarc-shaped segment around the second axis, a second substantially linearpath segment between the second axis and the first axis, and a secondsubstantially arc-shaped segment around the first axis. The nozzle maybe configured to direct the fluid jet to contact the second bucket inthe first substantially linear path segment of the second path such thatthe second fluid jet does not contact the second bucket in the secondsubstantially linear path segment of the second path.

The turbine system may further include a turbine blade, with the firstbucket being connected to a first end of the turbine blade (e.g., at acrossbeam) and the second bucket being connected to a second end of theturbine blade. The first bucket and the second bucket may be, forexample, hydraulically self-centering.

The turbine system may also include a moving structure with the turbineblade connected to the moving structure. In an embodiment, the turbineblade is connected to the moving structure at its mid-span such that thefirst end of the turbine blade and the second end of the turbine bladeare cantilevered. The moving structure may be, for example, a belt.

The nozzle may be positioned below a horizontal plane extending betweenthe first axis and the second axis. The nozzle may also direct the fluidjet outward to contact the first bucket and the second bucket. Forexample, the nozzle may direct the fluid jet outward to contact thefirst bucket at an angle with respect to the first substantially linearpath segment, the angle in a range from approximately 25° toapproximately 35°. A speed of the fluid jet may be greater than a speedof the bucket.

In an embodiment, a linear turbine system may include a first shaftextending along a first axis; a second shaft extending along a secondaxis, the second axis being separated from and substantially parallel tothe first axis; a plurality of buckets that travel a first continuouspath around the first shaft and the second shaft along a first plane,the first path including a first substantially linear path segmentbetween the first axis and the second axis, a first substantiallyarc-shaped segment around the second axis, a second substantially linearpath segment between the second axis and the first axis, and a secondsubstantially arc-shaped segment around the first axis; a nozzleconfigured to direct a fluid jet to contact the plurality of buckets inthe first substantially linear path segment; and a depower systemconfigured to cause rapid degradation of efficiency of the turbinesystem at an over-speed condition. In an embodiment, the depower systemmay include a deflector with the deflector arranged to selectivelydivert a portion of the fluid jet away from the bucket. The deflectormay include a pivot plate. The pivot plate may be arranged between thenozzle and the plurality of buckets. In another embodiment, the depowersystem may include a deflector arranged exterior to the plurality ofbuckets to direct fluid that exits one of the plurality of buckets intoa rear surface of an adjacent bucket. The linear turbine system mayfurther include a control system to control the depower system inincrements.

In an embodiment, a method of depowering a linear turbine system mayinclude distributing, via a nozzle, a jet of fluid to a plurality ofbuckets of a linear turbine system causing the plurality of buckets totravel a path around a first axis and a second axis; and depowering thelinear turbine system by rapidly degrading an efficiency of the linearturbine system. The method may further include actuating a flowdeflector of the linear turbine system such that the deflectorselectively diverts a portion of the jet of fluid away from theplurality of buckets. The method may also include pivoting a deflectorplate arranged between the nozzle and the plurality of buckets to divertthe portion of the jet of fluid. Alternatively, the method may includeactuating a flow deflector arranged exterior to the plurality of bucketsto direct fluid that exits one of the plurality of buckets into a rearsurface of an adjacent bucket. In addition, the method may includedepowering the linear turbine system by an efficiency increment.

The linear turbine bucket may be configured as an attachment to aturbine blade. In an embodiment, a linear turbine bucket may include afront surface having a concave curvature to receive a fluid jet from afirst direction and turn the fluid jet toward a second direction and arear surface to connect the linear turbine bucket to the linear turbineblade (e.g., at a crossbeam). A cross-section of the concave curvaturemay include, for example, a conic curve. The linear turbine bucket mayinclude a reinforced rib, the reinforced rib being positioned along acenterline of the bucket and being configured to receive a fastener toattach the bucket to the turbine blade. Alternatively, the linearturbine bucket may be integral with the turbine blade. A projectivediscriminant of the conic curve, also known as the rho value of theconic, is a range from approximately 0.2 to approximately 0.6. Thelinear turbine bucket may include a rounded leading edge. Othercomputational geometric surfaces are contemplated.

With a linear turbine bucket having a base; a top; a left side; and aright side, the fluid jet may be configured to enter the bucket at thebase and exit the bucket at the top, where a bucket width extends fromthe left side to the right side. The bucket width may have a range, forexample, from approximately 100 mm to approximately 1000 mm. The bucketwidth may have a range, for example, from approximately 110 mm toapproximately 500 mm. The bucket width may have a range, for example,from approximately 110 mm to approximately 130 mm. In an embodiment, thebucket ratio of the width to the size of a height of the fluid jet is arange from approximately 2 to approximately 6, wherein the height of thefluid jet extends along a width direction and the bucket width extendsalong the width direction. As used herein, “height” is not limited to avertical orientation with respect to ground. It may be a generalmeasurement, as measured with respect to the width direction of thebucket as discussed herein and described in the figures. The linearturbine bucket may also include a ramp on the rear surface, the rampincluding an edge to separate the fluid jet from the rear surface.

In an embodiment, a linear turbine may include a turbine blade (e.g.,blade, which may include a crossbeam) to travel a path around a firstaxis and a second axis parallel to the first axis; and a bucketconnected to the blade at a bucket rear surface, the bucket including afront surface having a concave curvature to receive a fluid jet from afirst direction and turn the fluid jet toward a second direction. Theconcave curvature may be a conic curve, a projective discriminant of theconic curve (i.e., “rho” value) being a range from approximately 0.2 toapproximately 0.6. The projective discriminant of the conic curve may bein a range from approximately 0.3 to approximately 0.5. The projectivediscriminant of the conic curve may be in a range from approximately0.35 to approximately 0.6. The concave curvature may include multipleconic curves, each having a projective discriminant within the aboverange.

The linear turbine bucket may include a base; a top; a left side; and aright side, and is configured such that the fluid jet enters the bucketat the base and exits the bucket at the top, and a bucket width extendsfrom the left side to the right side. The linear turbine bucket may alsoinclude a rounded leading edge. The bucket width may be, for example,approximately two to six times the size of a height of the fluid jet,where the height of the fluid jet extends along a width direction andthe bucket width extends along the width direction. The linear turbinebucket further comprising a reinforced rib, the reinforced rib beingpositioned along a centerline of the bucket and being configured toreceive a fastener to attach the bucket to the blade. The linear turbinebucket may include a ramp on the bucket rear surface, the ramp includingan edge to separate the fluid jet from the rear surface. The linearturbine bucket may be attached to a blade to mount on a linear turbine.Alternatively, the linear turbine bucket may be integral with theturbine blade.

In an embodiment, a linear turbine system may include a first shaft; asecond shaft separated from and substantially parallel to the firstshaft; a movable structure that travels a continuous path around thefirst shaft and the second shaft along a first plane; a plurality ofbuckets connected to the movable structure; and a nozzle configured todirect a fluid jet to contact the plurality of buckets, wherein theplurality of buckets are shaped to direct the fluid jet away from themovable structure. The linear turbine system may further include a firstblade attached to the movable structure and including one of theplurality of buckets connected to a first end and one of the pluralityof buckets connected to a second end, wherein the plurality of bucketsare shaped to direct the fluid jet away from the first blade. The firstblade may have a central portion attached to the movable structure; afirst intermediate portion positioned between the central portion andthe first end, the first intermediate portion being angled toward aplane that extends between the first shaft and the second shaft.

The first end may include a first tab that is approximatelyperpendicular to the first intermediate portion, the one of theplurality of buckets connected to the first end being attached to thefirst tab. The first blade may further include a second intermediateportion positioned between the central portion and the second end, thesecond intermediate portion being angled toward the plane that extendsbetween the first shaft and the second shaft. The second end may includea second tab that is approximately perpendicular to the secondintermediate portion, the one of the plurality of buckets connected tothe second end being attached to the second tab.

The linear turbine system may further include a second blade attached tothe movable structure and including one of the plurality of bucketsconnected to a first end and one of the plurality of buckets connectedto a second end, wherein the plurality of buckets are shaped to directthe fluid jet away from the second blade. The second blade may beseparated from the first blade by a blade or bucket separation distance.As shown in various figures, beginning with FIG. 4, a bucket separationdistance may be denoted by “S”. The ratio of the bucket axial chord “C”to the bucket separation distance S (i.e., C/S, denoted as “solidity”)may be a range from approximately 0.9 to approximately 3. The first arcshaped path segment and second arc shaped path segment may be ofsubstantially equal diameter. The size of this diameter may be betweenapproximately 1.5 and approximately 4 times larger than the bucketwidth. In some embodiments, the arc shaped path segments maysubstantially correspond to the dimensions of the sprockets, such thattheir diameters are coincident, or substantially coincident. Similardimensions may be defined by a blade or bucket separation distance. Thefirst shaft may be separated from the second shaft by a shaft separationdistance, the shaft separation distance being a range from approximately1.3 to approximately 5 times larger than the diameter of the arc shapedpath segments. The first shaft may be separated from the second shaft bya shaft separation distance, the shaft separation distance being a rangefrom approximately 1.5 to approximately 4 times larger than the diameterof the arc shaped path segments. The first shaft may be separated fromthe second shaft by a shaft separation distance, the shaft separationdistance being a range from approximately 2 to approximately 5 timeslarger than the diameter of the arc shaped path segments.

Solidity values may be selected to positively affect efficiency, and arescalable to differing installation requirements.

The linear turbine system may further include a roller or other supportmechanism or system positioned between the first shaft and the secondshaft to decrease an unsupported span of the movable structure. Thelinear turbine system may also include a tensioner to maintain tensionin the movable structure. The tensioner may have a movable plateconnected to the second shaft, the movable plate being configured tomaintain the second shaft as substantially parallel to the first shaftand a pushing mechanism to push the movable plate away from the firstshaft. The pushing mechanism may include a spring.

The first blade may be connected to the moving structure at its mid-spansuch that the first end of the first blade and the second end of thefirst blade are cantilevered. The moving structure may be a belt, forexample. The nozzle may be positioned below a horizontal plane extendingbetween the first axis and the second axis. The nozzle may direct thefluid jet outward to contact the plurality of buckets. The nozzle maydirect the fluid jet outward to contact the plurality of buckets at anangle with respect to a first substantially linear path segment of theplurality of buckets between the first shaft and the second shaft, theangle having a range, for example from approximately 25° toapproximately 35°. A speed of the fluid jet may be greater than a speedof one of the plurality of buckets.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and form a partof the specification, illustrate embodiments of the present inventionand, together with the description, further serve to explain theprinciples of the invention and to enable a person skilled in thepertinent art to make and use the invention.

FIG. 1 is a perspective view of a linear turbine system according to anembodiment.

FIG. 2 is a top view of the linear turbine system shown in FIG. 1.

FIG. 3 is a schematic side view of the linear turbine system accordingto an embodiment.

FIG. 4 is a schematic sectional view of the linear turbine systemaccording to an embodiment.

FIG. 5 illustrates velocity vectors relative to a linear turbine bucketaccording to an embodiment.

FIG. 6 is a plot of linear turbine efficiency as a function of speedratio ν and jet angle α₁, assuming a friction factor k=0.9 and exitangle β₂=10°.

FIG. 7 is a plot of inlet angle vs. linear optimal speed ratio,efficiency, specific speed, and runaway multiple when operated atoptimal conditions.

FIG. 8 illustrates the tradeoff between specific speed and efficiency.

FIG. 9 illustrates the sensitivity of optimal speed ratio to variationin bucket loss coefficient k, assuming α₁=33° and exit angle β₂=10°.

FIG. 10 illustrates a nozzle arrangement.

FIG. 11 illustrates a nozzle arrangement.

FIG. 12 illustrates a nozzle arrangement.

FIGS. 13 and 14 depict plots of velocity angle as shaded contour linesthat correspond to nozzle arrangements shown in FIGS. 11 and 12,respectively. The shading of the light effect is solely for graphicalclarity.

FIGS. 15 and 16 plot jet angle contours, as well as a profile at thecenterline as shown in FIGS. 11 and 12, respectively.

FIGS. 17-19 show streamlines of flow velocity for an exemplary nozzlearrangement.

FIG. 20 is a partial cross-sectional view of a system including a nozzlewith a −5° jet angle according to an embodiment.

FIG. 21 is a partial cross-sectional view of a system including a nozzlewith a +5° jet angle according to an embodiment.

FIG. 22 is a plot of bucket efficiency vs. nozzle angle with respect tohorizontal.

FIG. 23 illustrates a linear turbine and a nozzle arrangement having aslide gate according to an embodiment.

FIG. 24 shows a partial perspective view of a nozzle arrangement havinga slide gate according to an embodiment.

FIG. 24A shows a partial cross-sectional view of a nozzle arrangementhaving a slide gate according to the embodiment shown in FIG. 24.

FIGS. 25-29 illustrates jet angle contours at different slide gatepositions.

FIG. 30 illustrates profile at the centerline at different slide gatepositions.

FIGS. 31-33 plot various parameters vs. slide gate position.

FIG. 34 is a plot of relative efficiency vs. Q/Q_(max) (flow/best flow)for a slide gate.

FIG. 35 is a plot of efficiency vs. the ratio of jet height to bucketwidth.

FIG. 36 is a plot of efficiency vs. Q/Q*.

FIG. 37 is a plot of efficiency vs. jet angle.

FIGS. 38, 39, and 40 show an exemplary bucket design for a linearturbine, with FIGS. 39 and 40 illustrating a partial cascade ofexemplary buckets, their dimensional relationship, illustration ofsolidity, and fluid illustration from a CFD simulation showing the pathof fluid once it impinges upon a bucket.

FIGS. 41-45 a/b show an exemplary bucket design for a linear turbine.

FIGS. 46-49 are schematic views of an exemplary crossbeam design for alinear turbine.

FIG. 50-54 are schematic views of an exemplary crossbeam and bucketassembly (e.g., turbine blade) for a linear turbine.

FIG. 55 is a top view a linear turbine system configured as a compactarrangement.

FIG. 56 is a side view of a linear turbine chassis and take-up system.

FIG. 57 is a schematic view illustrating an exemplary installation of alinear system including a sealed housing.

FIGS. 58a-58d show a turbine system with no deflector, a turbine systemwith a jet deflector, a turbine system with a swamper, and a turbinesystem with a deflector jet, respectively, according to variousembodiments.

FIG. 59 is a perspective view of a linear turbine according to a dualdistributor (e.g., upper and lower distributor) embodiment.

FIG. 60 is a schematic side view of a linear turbine shown in FIG. 59.

FIG. 61 is a cross-sectional side view of a linear turbine shown in FIG.59.

FIG. 62 is a perspective view of a linear turbine having a split-chassisarrangement.

FIG. 63 is a perspective view of a linear turbine having a rollerbearing arrangement.

FIG. 64 is a perspective view of a linear turbine according to a linearPelton embodiment.

FIG. 65 is a perspective view of a linear turbine according to aninward-flow embodiment.

FIG. 66 shows a view of a linear turbine according to a bi-directionalembodiment.

FIG. 67 is a schematic perspective view of a nozzle arrangement have awicket gate according to an embodiment.

FIG. 68 depicts application ranges for various type of hydraulicturbomachines, a plot of as Q vs. H with lines of constant powerdetermined assuming η₀=0.8.

FIG. 69 is a plot of efficiency vs. Q/Q₀ for various types of turbines.

FIG. 70 is a schematic side view of a conventional Pelton turbine.

FIG. 71 is a schematic sectional view of a conventional Pelton turbinewith velocity vectors.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of a system, method, and apparatus for producing power froma fluid source (e.g., fluid impulse source) addresses a significantchallenge in the capture of low-head fluid power resources, such aslow-head hydropower. The linear turbine may be configured for use atdrops in elevation in natural waterways (e.g., river) or constructedwaterways (e.g., a canal). The linear turbine enables power to beproduced with high efficiency, and maintains high efficiency despitechanges in the amount of fluid passing through the engine.

Embodiments disclosed have numerous advantages over prior turbinedesigns. The implementation of hydraulic impulse turbine principles inthe design and operation of embodiments discussed allows the engine tomaintain high efficiency over a broad range (low to high) of flows atlow head. Embodiments of the linear turbine system disclosed herein mayachieve efficiency of greater than or equal to 85%. Embodiments of thelinear turbine system may be capable of generating over 1 MW at 10meters (“m”) head.

By way of background, turbines convert the kinetic energy of a movingfluid to useful shaft work by the interaction of the fluid with a seriesof buckets, paddles, or blades arrayed about the circumference of arunner. Two main classes of turbines (impulse and reaction) have manyvariations.

Reaction machines utilize a pressure drop across the moving blades. Areaction turbine develops power from the combined action of pressure andmoving water. Reaction turbines are generally used for sites with lowerhead and higher flows than compared with the impulse turbines.

In an impulse machine, the entire pressure drop occurs before the fluidinteracts with the moving blade, so pressure is constant across themoving blades. Conventional impulse turbines include a runner designedto rotate about a single axis when the force of a stream of water hitsblades or buckets that are mounted around the perimeter of a runner.Typically, there is no suction on the outlet (e.g., down) side of theturbine, and the water falls out the bottom of the turbine housing afterleaving the buckets. Conventional impulse turbines are generallysuitable for high head, low flow applications.

The Pelton turbine is the most common type of hydraulic impulse turbinein use today. FIGS. 70 and 71 depict a conventional Pelton turbinearrangement in a case 312. The Pelton turbine has one or more nozzles302 that are positioned to orient a jet of water 303 tangential to arotatable wheel. A plurality of Pelton buckets 310 are mounted about theperimeter of the rotatable wheel. Jet 303 impacts the plurality ofPelton buckets 310 on the wheel at their centers. The impact on theplurality of Pelton buckets 310 results in a torque, causing the wheelto rotate a coaxial drive shaft 308. The drive shaft 308 may in turndrive a generator to produce electricity. Flow rate through the nozzleis adjustable through use of a valve, such as a spear valve. Anadjustable spear 306 has a tapered point which cooperates with thenozzle 304 to act as a control valve to adjust the flow of the waterjet.

The curvature of the Pelton buckets is chosen so that the exiting flowis turned to a direction nearly opposite to that of the incoming jet. Apractical limit of this turning angle is about 165° in order to avoidsubsequent buckets splashing against the outflow. Even with thislimitation, Pelton turbines today typically have peak efficiency ofabout 0.9 (about 90%), with multi jet Pelton wheels (multiple individualjets arranged around the wheel to simultaneously push different bucketson the wheel) having efficiency exceeding 0.92. However, these turbineshave the smallest specific speed of any common turbine, and thus arelimited in use to very high head, e.g., over 90 meters, and frequentlyover 1,000 meters. Turgo turbines behave in a manner similar to Peltonturbines, but allow increased specific speed by allowing flow tointersect multiple sequential blades at once. However, Turgo turbinesare still medium-to-high-head machines, with most units being utilizedabove 50 meters of head.

Embodiments discussed herein overcome many of the shortcomings of Peltonand Turgo turbines. As discussed below, the linear turbine (e.g., linearturbine system) may be optimized to work efficiently over a large rangeof head (for example, from approximately 20 meters head to approximately2 meters head). Buckets may be mounted symmetrically on either side of acentral chassis structure, about parallel shafts. The linear path oftravel may be orientated in a generally horizontal direction.

The linear turbine is preferably installed such that the lowest buckets(as installed at an installation site) are located above the tailwater.The linear turbine may be equipped to operate within a case, chamber orhousing capable of maintaining a vacuum relative to the ambientatmosphere, enabling the turbine to avoid loss of head below the turbineby locally elevating the tailwater inside the case. This results in thetailwater inside the case being at a level higher than the ambientsurrounding tailwater. The linear turbine avoids cavitation risk due toits operation as an impulse turbine with relatively low suction head.

These and other features allow the turbine to be installed abovetailwater in a way that substantially reduces civil works costs.Moreover, a free jet nozzle and single-stage interaction of the jet withthe buckets causes the majority of resultant forces on the blades(imparted in the buckets) to be directed substantially in the directionof blade travel. By mounting buckets symmetrically about a bifurcatednozzle on the turbine blade, such as through a crossbeam, loads alongthe length of the beam are resolved into tension within the beam. Bylocating the buckets such that the center of pressure imparted by thefluid on each bucket is substantially close to the pitch line of thebelt, moment loads are minimized, allowing the blade-to-belt attachmentmechanism to become simple, primarily being designed to pass shear fromthe blade, into the belt. The moving impulse blades experience littledrag force, so frictional losses are minimal. In some embodiments, thecrossbeam and buckets may be modular, such that buckets having differentsizes and shapes may be interchangeable for a given turbine.

The linear turbine may be designed without tight clearances betweenmoving blades and stationary components, and may also implement a simpleflow control. In some embodiments, the linear turbine may include arapid depowering system. The linear turbine design is debris tolerantand thus robust to certain environmental conditions. In addition, thelinear turbine produces power while maintaining pressure and velocityconditions within the fluid commensurate with biological organisms'vital needs. For example, the linear turbine design may be“fish-friendly” when utilized in a water environment.

A linear turbine system as described herein may utilize a nozzle andbucket system for efficient power conversion, without requiring a drafttube, stators, wicket gates, stay vanes, or guide vanes. Just as aconventional Pelton bucket's role is to harness the energy from the freejet (effectively reversing the direction of the free jet), the same istrue of the linear turbine bucket. Similarly, the nozzle's role is toconvert pressure (potential energy) into velocity (kinetic energy) withminimal loss, and orient the fluid jet toward the buckets at an optimalangle with high uniformity. As used herein, when referring to the linearturbine system, “bucket” denotes a portion of the turbine blade, such asa curved surface, that receives fluid and redirects it (converting theenergy from the fluid). This is in contrast to water wheels, forexample, which receive fluid and hold fluid as the water wheel turns.

The jet utilized in a conventional Pelton turbine has a circularcross-section along the jet's direction of travel. In some embodiments,in a linear turbine as described herein, the jet may be rectilinear, orhave a substantially rectangular cross-section (either as shown by thenozzle outlet, or direction of travel of the jet exiting the nozzle).The jet cross-section may have a predetermined length to accommodate adesired number of buckets (or bucket modules) mounted on a powertrainconveyor, such as a belt, chain, track, or direct drive system. Incontrast to the conventional Pelton arrangement, where an individual jetis limited to providing an impulse to one or two buckets at a time, asingle, extended jet, such as a rectilinear jet, may be configured tosimultaneously provide impulses to a large number of buckets (due to thelinear nature of the turbine). As described below, two or morerectilinear jets may be utilized to multiply the already large number ofimpulses. Like a conventional Pelton turbine, the linear turbine systemsdescribed herein may be single-stage impulse turbine systems, that is,an impulse transfer of energy from the fluid flow to the turbine occursin a single stage. The linear turbines discussed herein may also beconfigured as multi jet turbines, and similarly may be configured asmulti-stage turbines.

Although specific configurations and arrangements are discussed, itshould be understood that this is done for illustrative purposes only. Aperson skilled in the pertinent art will recognize that otherconfigurations and arrangements can be used without departing from thespirit and scope of the present invention. It will be apparent to aperson skilled in the pertinent art that this invention can also beemployed in a variety of other applications.

It is noted that references in the specification to “one embodiment,”“an embodiment,” “an example embodiment,” etc., indicate that theembodiment described may include a particular feature, structure, orcharacteristic, but every embodiment may not necessarily include theparticular feature, structure, or characteristic. Moreover, such phrasesdo not necessarily refer to the same embodiment. Further, when aparticular feature, structure or characteristic is described inconnection with an embodiment, it would be within the knowledge of oneskilled in the art to effect such feature, structure or characteristicin connection with other embodiments whether or not explicitlydescribed.

As used herein, ranges are inclusive of endpoints.

As used herein, “substantially,” and “about,” when used in combinationwith ranges, are used to include variation of around +/−5% of therecited value.

Referring to FIGS. 1-4, one embodiment of a linear turbine or linearturbine system 100 is implemented as a hydroelectric engine forproducing electric power from a fluid impulse source. FIG. 1 shows apartial perspective view of linear turbine system 100 with a portionremoved to illustrate the underlying chassis. Unlike a conventionalPelton turbine which has a single axis of rotation, linear turbinesystem 100 is arranged having a first shaft 128 extending along a firstaxis 112 and a second shaft 129 extending along a second axis 113 (FIG.4). Second axis 113 is separated from and substantially parallel tofirst axis 112. This configuration creates substantially linear pathsegments 140, 142, which are utilized for impulse power. Water level1000 is shown within the system, at a higher level than ambient waterlevel outside the system due to the partial relative vacuum created bythe system's operation.

As shown in FIGS. 1-4, linear turbine system 100 includes a firstplurality of buckets 110 to travel a first continuous path (indicated byarrows 140, 141, 142,143) around first shaft 128 and second shaft 129with the path substantially confined to a first plane perpendicular tofirst axis 112 and second axis 113. In some embodiments, the fluid maybe discharged in the first linear path segment. Buckets 110 may beconfigured as blades, or attached to an additional element that makes upa finished blade, such as crossbeam 138. In some embodiments, crossbeam138 may be a portion of a blade. The first path 140, 141, 142,143includes a first substantially linear path segment 140 between firstaxis 112 and second axis 113; a second substantially linear path segment142 between first axis 112 and second axis 113; a first substantiallyarc-shaped segment 141 connecting first linear path segment 140 tosecond linear path segment 142; and a second substantially arc-shapedsegment 143 connecting second linear path segment 142 to first linearpath segment 140. First axis 112 and second axis 113 are separated by aaxial separation distance 144 along a horizontal direction and in theplane of first continuous path 140, 141, 142,143 as measured from thecenterlines of the shafts 112/113. Thus, axial separation distance 144substantially defines the length of linear path segments 140, 141. Aswill be appreciated by a person of ordinary skill in the art, the term“substantially linear” with regard to linear path segments 140, 141 isintended to account for minor variances in the linear path due tomechanical constraints on the system, such as a measurement of sag dueto gravity. As discussed herein, a tensioning system may be implementedwith the linear turbine system, in part, to minimize such constraints.

In some embodiments, first linear path segment 140 is designed to besubstantially linear so as to engage a linear (e.g., substantiallyrectilinear) free jet. In some embodiments, second linear path segment142 needed not be so confined if second linear path segment 142 is notsimilarly utilized for free jet impulse power. Instead of second linearpath segment 142, a non-linear path segment (e.g., arcuate), additionalpath segments (e.g., arcuate and linear), or no path segment (e.g.,directly linking first and second arc-shaped segments 141, 143) may beutilized.

Linear turbine system 100 also includes a second plurality of buckets120 symmetrically arranged to first plurality of buckets 110. Likebuckets 110, buckets 120 are configured to travel a continuous patharound first shaft 128 and second shaft 129 with the path substantiallyconfined to a plane perpendicular to first axis 112 and second axis 113(and thus parallel to first path 140, 141, 142, 143). Like first path140, 141, 142, 143, the path for buckets 120 similarly includes a firstsubstantially linear path segment between first axis 112 and second axis113; a second substantially linear path segment between first axis 112and second axis 113; a first substantially arc-shaped segment connectingfirst linear path segment to the second linear path segment; and asecond substantially arc-shaped segment connecting the second linearpath segment to first linear path segment.

In the embodiment shown in FIGS. 1-4, first plurality of buckets 110 andsecond plurality of buckets 120 may be mechanically linked so as torotate together on first shaft 128 second shaft 129 about first axis 112and second axis 113. Linkages may be in the form of dually cantileveredcrossbeams 138, which couple one individual bucket from each of firstplurality of buckets 110 and second plurality of buckets 120 by fixedlymounting a bucket on either end of the crossbeams 138. Crossbeams 138are center mounted to a powertrain that is configured to constrain thecrossbeam and bucket assemblies along first path 140, 141, 142, 143.Details regarding embodiments of the buckets and crossbeams that may beutilized with linear turbine system 100 are described below. Crossbeams138 may be attached directly the belt, (e.g., requiring no bearings orplatforms themselves), in some embodiments.

As illustrated in FIGS. 1-4, a nozzle/nozzle system may be employed toprovide impulse power to linear turbine system 100. A nozzle 122 may bepositioned between the first continuous path 140, 141, 142, 143 of firstplurality of buckets 110 and the second continuous path (parallel tofirst path 140, 141, 142, 143) of second plurality of buckets 110.Nozzle 122 is configured to direct a first fluid jet to contact firstplurality of buckets 110 along first linear path segment 140. Nozzle 122is also configured to direct a second fluid jet to contact secondplurality of buckets 120 along a linear path segment. Nozzle 122 isconfigured such that fluid jet may be a free jet. In addition, nozzle122 is configured to generate well-conditioned flow from a penstock orinlet to two nozzle outlets. To create separate free fluid jets fromeach nozzle outlet and well-conditioned flow within the nozzle, nozzle122 includes a bifurcation proximal to a nozzle inlet. In someembodiments, the speed of the fluid jet is greater than a speed of thebucket. In some embodiments, the system may discharge a portion of thefluid at points along the first or second linear path segment. In someembodiments, the system may discharge all or substantially all of thefluid at points along the first or second linear path segment. In someembodiments, the orientation of the system is such that the fluid isdischarged from the buckets in the first or second linear path at anobtuse angle relative to the direction of travel.

Fluid, such as water, may flow into the linear turbine through adistributor, such as penstock or inlet 121, which is connected to aninlet of a nozzle 122. In an embodiment, the linear turbine system mayinclude two distributors to direct fluid into buckets on complimentarysides of the linear turbine. In some embodiments, first and secondoutlets of nozzle 122 are substantially symmetrical (outlet 127 isillustrated in FIG. 3). Fluid exits first and second outlets into thetraveling the plurality of buckets 110, 120 (e.g., at an acute angle).As illustrated by FIGS. 3 and 4 as well as others, first and secondoutlets may be rectilinear openings that are parallel to a plane ofcontinuous path 140-143. Nozzle 122 is configured to direct the firstfluid jet to contact the first plurality of buckets at a non-zero (e.g.,non-orthogonal) angle.

In some embodiments, nozzle 122 directs the first rectilinear jet offluid at an angle α with respect to a plane that extends along the firstsubstantially rectilinear opening at outlet 127. The opening may beparallel and near to the plane of bucket travel path 140-143, such thatthe first rectilinear jet also makes an angle α with the plane of buckettravel path 140-143. The angle is in a range from approximately 0° toapproximately 50°. In other embodiments, the angle has a range fromapproximately 25° to approximately 35°. In yet other embodiments, fluidexits first and second outlets at an angle α in a range fromapproximately 8° to approximately 18°, such as approximately 10° toapproximately 15°. In some embodiments, the fluid interacts with acascade of buckets. In some embodiments, fluid exits a bucket at anangle β in a range from approximately 8° to approximately 18°, such asapproximately 10° to approximately 15°. In another aspect, a free jetexits the distributor/nozzle at an angle of approximately 10°.

As used herein, β denotes the relative flow angle measured from the samevector as α. β₁ denotes the relative flow angle corresponding to theangle aiding in the definition of the likely ideal angle of the bucket'sleading edge. β₂ denotes the relative flow angle aiding in thedefinition of the likely ideal angle the likely ideal angle of thebucket's trailing edge.

A velocity of the first rectilinear jet of fluid may be approximatelyequal to a velocity of the second rectilinear jet of fluid. In anembodiment, the first substantially rectilinear opening extends along afirst plane and the second substantially rectilinear opening extendsalong a second plane such that the first plane and the second plane aresubstantially parallel. In other embodiments, the first substantiallyrectilinear opening extends along a first plane, the first plane havingan angle in a range from approximately −5° to approximately 15° withrespect to horizontal. In other embodiments, the angle has a range fromapproximately −5° to approximately 10°. In other embodiments, the anglehas a range from approximately −5° to approximately 5°.

The relationships are shown further in FIG. 5, showing velocity vectorsrelative to a linear turbine bucket according to an embodiment,including relative velocity W₂.

The powertrain of linear turbine system 100 or linear turbine system 100itself is mounted on a base, such as plinth 160. The powertrain mayinclude a belt 134 operating about sprockets/pulleys 136, 137,constrained to a “stadium” or oval path resembling a racetrack. In someembodiments, the belt may be configured as a chain for example,reinforced belt, polymeric belt, or cables. In some embodiments, thepowertrain may be a direct drive mechanism. Belt may be a toothed belt,for example, and pulleys may include teeth corresponding to the beltteeth. As the energy from the jet is utilized by the buckets/blades, thebucket/blades drive the belt, which in turn drives sprockets 136, whichin turn drive one or more generator shafts 128, 129 at either end ofbelt 134. As shown in FIGS. 1-2, a speed increaser 150 is mounted onshaft 128 and is linked by a belt to an electric generator 152. Shafts128, 129 may be attached to sprockets 136, 137 which may turn onbearings attached to a common baseplate. In some embodiments, shafts128/129 may be generally horizontally positioned. In some embodiments,shafts 128/129 may be generally vertically positioned. In someembodiments, shafts 128/129 may be positioned at an angle betweenhorizontal and vertical.

In some embodiments, the linear turbine may have less than ten movingparts (excluding the buckets/bucket assemblies). For example, a linearturbine may include a single belt turning around two sprockets. Thesprockets may be attached to a shaft which can turn a generator. Thelinear turbine may also include crossbeams attached directly to the beltwithout the need for bearings with moving parts. The buckets can beattached to the ends of the crossbeam to receive incoming fluid flow.The linear turbine can include smaller buckets to more evenly distributeloads and better match crossbeam and bucket strength with belt strength.

The flow capacity and power of the linear turbine system 100 isadjustable for a particular project, by changing the number ofbuckets/bucket modules in the path, thus changing the length of themachine. This flexibility allows much larger flow per turbine than aconventional Pelton unit. Multiple nozzles can be used to increase flowrate for a given runner. The linear turbine system can utilize one sidenozzle, or more, which applies increased flow rate across both linearspans for power production.

In operation, a fluid flow 124 from fluid source (such as a river orcanal) enters a penstock or intake duct 121. Flow 124 then passesthrough nozzle 122 which accelerates, bifurcates, and redirects flow 124to generate two free jets. The acceleration, bifurcation, andredirection may be simultaneous. Two nozzle outlets have a substantiallyrectilinear shape (e.g., formed from substantially straight lines) tofor rectilinear shaped (e.g., rectangular shaped) free jets. Othernozzle outlet shapes are also contemplated, such as rectilinear shapeswith rounded corners, circular, elliptical, or oval shapes, etc. Eachfree jet is directed toward and provides an impulse (force applied for aperiod of time) to a plurality of buckets 110, 120. Each free jetsimultaneously impacts more than two buckets. For example, each free jetis configured to simultaneously impact/impinge upon 10-20 buckets. Inanother example, each free jet is configured to simultaneouslyimpact/impinge upon 20-30 buckets. In another example, each free jet isconfigured to simultaneously impact/impinge upon 30-40 buckets.Additional blades and or buckets are contemplated, such as 30, 45, 50,55, 60, 80, 103, and 105. One of the benefits of the linear turbinedesign is that the design can easily scale up for larger flows; thesystem may be lengthened by increasing an axial separation distance 144and adding additional bucket assemblies. If desired, additional supportshafts/axles may also be added to accommodate additional bucketassemblies.

Fluid flow 124 provides a controllable impulse to linear turbine system100 which drives plurality of buckets 110, 120 about axes 112, 113.Plurality of buckets 110, 120 transfer this power, via crossbeams 138,belt 134, and sprocket 136, to drive shaft 129. Drive shaft 129transfers power to the speed increaser 150, which in turn drives anelectric generator 152.

In some embodiments, one or more of the shafts is coupled to a secondarystructure to impart useful work (recovered through the operation of thelinear turbine). In some embodiments, a shaft is coupled to a hydraulicpump, for example, or mill.

A slide gate or similar apparatus may be used to control the length ofthe outlet and accordingly the number of buckets impacted by the freejets to accommodate decreases in flow. For an under-mounted nozzle 122,the fluid from the free jet is simply directed away from the turbine bythe bucket shape and falls to form a tailwater 162. Tailwater 162 maythen rejoin the original water source. The linear turbine design is not,however, just applicable to under-mounted nozzle arrangements, as atop-mounted may also be utilized with or without an under-mountednozzle.

The next section provides the theory and analysis behind the linearsystem, with certain relationships illustrated in FIG. 5.

Theory and Analysis

Flow exits a nozzle with mean velocity driven by the effective headH_(E)V ₁ =C _(ν)√{square root over (2gH _(E))}  (1)

where C_(ν) is the velocity coefficient of the nozzle.

The effective head, H_(E), is the head delivered at the nozzle, aftersubtracting losses such as pipeline friction and intake losses, from thegross head. The efficiency of the turbine is measured versus theeffective head H_(E), not the gross head H_(G).H _(E) =H _(G) −H _(f)  (2)

The ideal, or spouting, velocity, isV ₀=√{square root over (2gH _(E))}  (3)

The nozzle velocity coefficient C_(ν) is the ratio of the actual meanvelocity at nozzle exit, V₁, to the spouting velocity V₀

$\begin{matrix}{C_{v} = \frac{V_{1}}{V_{0}}} & (4)\end{matrix}$

Typical Pelton nozzle C_(ν) ranges from 0.98 to 0.99. Nozzle efficiencyis

$\begin{matrix}{\eta_{N} = \frac{V_{1}^{2}}{2{gH}_{E}}} & (5)\end{matrix}$

The complete turbine hydraulic efficiency is the ratio of worktransferred from the jet to the buckets (ΔW) to the available energygH_(E); it is also the product of the nozzle efficiency η_(N) and thebucket efficiency η_(B).

$\begin{matrix}{\eta_{h} = {{\frac{\Delta\; w}{g\; H_{E}}\left( \frac{\Delta\; w}{\frac{1}{2}V_{1}^{2}} \right)\left( \frac{\frac{1}{2}V_{1}^{2}}{g\; H_{E}} \right)} = {\eta_{B}\eta_{N}}}} & (6)\end{matrix}$

The work transferred from the jet to the buckets is expressed by Euler'sturbine equationΔW=UV _(1U) −UV _(2U)  (7)

Thus, the bucket efficiency can be expressed as

$\begin{matrix}{\eta_{B} = {\frac{\Delta\; w}{\frac{1}{2}V_{1}^{2}} = \frac{2\;{U\left( {V_{1\; U}V_{2\; U}} \right)}}{V_{1}^{2}}}} & (8)\end{matrix}$whereV _(1U) =V ₁ cos α₁  (9)V _(2U) =U−w _(2U) =U−kw ₁ cos β₂  (10)

Friction causes the relative velocity of flow at the bucket's outlet tobe lower than at its inlet, so thatw ₂ =kw ₁  (11)

Typical Pelton buckets k range from 0.8 to 0.9.

The operation of a linear turbine can be characterized in terms of theratio of bucket speed to jet speed ν

$\begin{matrix}{v = \frac{U}{V_{1}}} & (12)\end{matrix}$

In a linear turbine, the jet may enter the bucket cascade at a non-zeroinlet angle, α₁. The bucket's shape is chosen to turn the flow such thatit leaves with relative velocity angle β₂. For any combination of α₁,and β₂, there exists an optimal ν such that efficiency is maximized.

In comparison, conventional Pelton turbines represent a special case inwhich the inlet angle is 0°. The optimal blade-jet speed ratio of aconventional Pelton turbine is ν=0.5 since α₁=0 and η_(B)=2ν(1−ν)(1−kcos β₂); the optimal efficiency of a conventional Pelton turbine isη_(Bmax)=(1−k cos β₂)/2.

Using the law of cosinesw ₁=√{square root over (V ₁ ² +U ²−2 cos α₁ UV ₁)}  (13)

Given 9, and sinceU=νV ₁  (14)

w₁ can be foundw ₁=_(V1)√{square root over (ν²−2 cos α₁ν+1)}  (15)

Substituting Equation (15) into Equation (10), the expression for linearbucket efficiency can be written asη_(B)=2ν cos α₁−2ν²+2k cos β₂ν√{square root over (ν²−2ν cos α₁+1)}  (16)

The efficiency can be alternatively formulated in terms of a ratio ofblade speed to the peripheral speed, V_(U), rather than jet speed V₁.

$\begin{matrix}{{v^{+} = \frac{U}{V_{1\; U}}}\eta_{B} = {{2\; v^{+}{\cos\;}^{2}\alpha_{1}} - {2\; v^{+ 2}{\cos\;}^{2}\alpha_{1}}}} & (17) \\{{{+ 2}\; k\;\cos\;\alpha_{1}\cos\;\beta_{2}v^{+}\sqrt{1 + {{v^{+}\left( {v^{+} - 2} \right)}\;{\cos\;}^{2}\alpha_{1}}}}\;} & (18)\end{matrix}$

To determine the maximum efficiency, differentiate Equation (16) withrespect to ν

$\begin{matrix}{{\frac{d\;\eta_{B}}{dv} = {{{2\;{v\left( {\frac{k\;\cos\;{\beta_{2}\left( {{2\; v} - {2\;\cos\;\alpha_{1}}} \right)}}{2\sqrt{v^{2} - {2\; v\;\cos\;\alpha_{1}} + 1}} - 1} \right)}} + {2\left( \;{{\cos\;\alpha_{1}} + {k\;\cos\;\beta_{2}\sqrt{v^{2} - {2\; v\mspace{11mu}\cos\;\alpha_{1}} + 1}} - v} \right)}} = 0}}\;} & (19)\end{matrix}$

Dimensionless hydrodynamic coefficients for linear turbines may bere-derived for the linear turbine.

Head Coefficient:

$\begin{matrix}{C_{H} = {\frac{{gH}_{e}}{\omega^{2}D^{2}} = \frac{1}{8\; C_{v}^{2}v^{2}}}} & (20)\end{matrix}$

Flow Coefficient:

$\begin{matrix}{C_{Q} = {\frac{Q}{\omega\;{DA}_{t}} = \frac{1}{2v}}} & (21)\end{matrix}$

Power Coefficient:

$\begin{matrix}{C_{P} = {\frac{P}{\rho\;\omega^{3}D^{3}A_{t}} = \frac{\eta_{B}}{16\; v^{3}}}} & (22)\end{matrix}$

The turbine throat area is a function of the jet angleA _(t) =H _(j) L _(j) sin α₁  (23)

Where H_(j) is the jet height as shown in the figures, and L_(j) is thetotal length of the jet in the tangential direction.

Thus, A_(t)∝ sin α₁ and the power specific speed, C_(pss), can beexpressed in terms of the inlet jet angle

$\begin{matrix}{{\frac{D}{\sqrt{H_{j}L_{j}}}*C_{pss}} = \frac{\sqrt{C_{p}\sin\;\alpha_{1}}}{C_{H}^{5/4}}} & (24)\end{matrix}$

The turbine is able to maintain high efficiency across a wide range ofjet angles, with slight changes in the optimal speed ratio. For example,assuming bucket friction factor k=0.9 and bucket exit angle β₂=10°, thebucket efficiency only decreases from 0.94 at 0°, to 0.9 at a jet angleof 40° (FIG. 6).

FIG. 6 is a plot of linear turbine efficiency as a function of speedratio ν and jet angle α₁, assuming a friction factor k=0.9 and exitangle β₂=10°.

FIG. 7 is a plot of inlet angle vs. linear optimal speed ratio,efficiency, specific speed, and runaway multiple when operated atoptimal conditions.

FIG. 8 illustrates the tradeoff between specific speed and efficiency.

FIG. 9 illustrates the sensitivity of optimal speed ratio to variationin bucket loss coefficient k, assuming α₁=33° and exit angle β₂=10°.

An advantage of the disclosed linear turbine in comparison to theconventional Pelton turbine lies in its ability to accept a much largeramount of flow, within a small physical footprint. This can beunderstood by inspecting the relationship between power specific speed,and the jet angle α₁. Linear turbine bucket efficiency decreases onlyweakly as α₁ increases, while the throat area and thus the powerspecific speed C_(pss) increase substantially at larger inlet angles(FIG. 7). The choice of optimal inlet angle will be a tradeoff, with theengineer choosing a balance between specific speed, and efficiency (FIG.8), which may be Pareto-optimal.

Generally, friction experienced by the bucket (e.g., bucket friction)has a large impact on efficiency. Additionally, an increase in bucketfriction results in a decrease in the optimal bucket-to-jet speed ratio.For example, a linear turbine configured with α₁=33° and β₂=10°, adecrease in k from 0.95 to 0.65 results in a decrease in bucketefficiency η_(B) from 0.95 to 0.75, and a decrease in ν* from 0.58 to0.53 (FIG. 9).

Nozzle Arrangement

Without a proper nozzle design, fluid flow may exhibit non-uniformdistribution of velocity down the length of linear travel of thebuckets. The nozzle design architecture described here allows veryuniform velocity distribution (variation approximately <3%) in the jetoutlet. Design parameters have been developed for proper sizing of thenozzle length as a function of the jet angle, distance from nozzleoutlet to bucket, and bucket chord width. The nozzle architecture allowsfor efficient (C_(ν)>0.95) conversion of pressure into kinetic energy,without any components such as guide vanes needed inside the flow path.In some embodiments, guide vanes or other flow-enhancement devices arecontemplated.

Turning to FIGS. 10-12, as shown in FIG. 10, a bifurcation 1026 within anozzle arrangement 1022 is located very close to the nozzle inlet 1025.Thus, a separation distance d between nozzle inlet 1025 and bifurcation1026 is desirably small, such as approximately 0.02 to approximately 2.5times the hydraulic diameter of the nozzle at the inlet cross-section.This allows for substantially uniform velocity at the two nozzle outlets1027 a, 1027 b.

FIG. 12 illustrates nozzle arrangement 1122 similar to the nozzlearrangement 1022. A separation distance d₂ between a nozzle inlet 1125and a bifurcation 1126 is kept small. A round-to-polygonal adaptersection 1123 is joined to funnel fluid flow 1124 from a penstock intonozzle 1122. One end of round-to-polygonal adapter section 1123 ismatched to the size and shape of the penstock. The other end is sizedand shaped to match nozzle inlet 1125 and joined to nozzle inlet 1125.FIGS. 17 (top view), 18 (rear view), and 19 (side view) plot streamlinesof velocity and contours for velocity angle for nozzle arrangement 1022,which exhibits well-conditioned flow having uniform or substantiallyuniform exit velocity angle across the entire nozzle exit. In someembodiments, the nozzle provides centrally delivered flow, that is,inward to outward flow. The outlet may be disposed at or near the bottomof the system. Furthermore, in some embodiments, the nozzle only acts ona straight, section of the belt, e.g., within one of the linear pathsegments disclosed and described herein.

FIG. 11 illustrates a comparative example of a nozzle arrangement 1222.Unlike nozzle arrangement 1122 in FIG. 12, a separation distance d₁between a nozzle inlet 1225 and a bifurcation 1226 is located muchfurther away, resulting in less than idealized pressure and velocitydistributions, and particularly undesirably large variations in nozzleexit angle α. A round-to-polygonal adapter section 1223 is joined tofunnel fluid flow 1224 from a penstock into nozzle 1222. One end ofround-to-polygonal adapter section 1223 is matched to the size and shapeof the penstock/inlet from the source. The other end is sized and shapedto match nozzle inlet 1225 and joined to nozzle inlet 1225. Duringtesting, while nozzle arrangement 1122 in FIG. 12 exhibited a velocitydistribution variation less than 3%, the nozzle arrangement 1222 in FIG.11 exhibited a velocity distribution variation greater than 10%.

Compared to the nozzle arrangement 1222, nozzle arrangement 1122 removesan intermediate tapering portion of the nozzle outlet, and widens thenozzle inlet accordingly. The “V”-shape at the end is steeper and tunedto provide maximum streamline parallelism. For the purposes ofcomparative testing further described below, the exemplary length ofnozzle arrangement 1122 was 402 mm, whereas the exemplary length ofnozzle arrangement 1222 was 545 mm, corresponding to 26% difference inlength.

Arranging the nozzle with a v-shaped inlet cross-section in which thebifurcation depth is driven by the total cross-sectional area of the jetoutlet allows for nozzles of longer and shorter dimension to be builtwithout significant change in performance.

The nozzle architecture may be adapted for use with differentmanufacturing methods. For example, straight-brake sheet metal or platefabrication may be used with a nozzle designed with prismatic-typesurfaces and sharp corners. Alternatively, if a molding or similarmanufacturing approach is utilized, smoothly rounded corners and anorganic manifold shape may be used, resulting potentially in lowerlosses.

The nozzle arrangements may be desirably configured such that a lengthof jet is matched to available linear travel of buckets (e.g., alonglinear path 140). The nozzle arrangements may also be configured togenerate uniform and/or parallel streamlines at all locations alongfluid flow. The nozzle arrangements may also be configured to produce ahigh velocity coefficient and thus a highly efficient and low lossdesign.

FIGS. 13 and 14 depict plots of velocity angle that correspond to nozzlearrangements in FIGS. 11 and 12, respectively, operating at the samehead (approximately 3.4 m). FIG. 13 illustrates velocity angle fornozzle arrangement shown in FIG. 11, which is characterized by a strongvariation in velocity angle along the length of the jet. Velocity angleat mid-span is roughly 40% higher than velocity angle at the entry andexit of the jet. FIG. 14 illustrates velocity angle for nozzlearrangement shown in FIG. 12, which accomplishes a major improvement inuniformity of velocity angle at the jet exit. Velocity angle varies byonly approximately 7%. along the length of the nozzle exit.

The performance of nozzle arrangements 1222 and 1122 may be summarizedusing standard C_(v)=V_(jet)/√(2gh) calculation, augmented by theimportant measure of uniformity of vU along the jet length.

The performance of nozzle arrangements 1222 and 1122 may be summarizedusing standard C_(v)=V_(jet)/√(2gh) calculation, augmented by theimportant measure of uniformity of vU along the jet length.

TABLE 1 nozzle arrangement 1222 (FIG. 11) 1122 (FIG. 12) P_(tot, in) Pa33285 33588.9 P_(tot, out) Pa 31100 31453.6 V_(jet) m/s 7.88 7.93 h, inM 3.4 3.43 C_(v) — 0.964 0.966 C_(v) ² — 0.931 0.933 vU, ends m/s 7.457.4 vU, midspan m/s 6.45 7.2 % delta — 0.127 0.025

More detailed analysis of flow angle uniformity for nozzle arrangements1222 and 1122 is shown in FIGS. 15 and 16. FIG. 15 plots jet anglecontours, as well as a profile at the centerline for nozzle arrangementof FIG. 11. FIG. 16 plots jet angle contours, as well as a profile atthe centerline for nozzle arrangement of FIG. 12. The x-axes arenormalized between FIGS. 15 and 16.

Nozzle Tilt

In the development of large linear turbines, for example, those capableof generating over 1 MW at 10 m head, an issue was discovered whichcould create problems in which the turbine efficiency strongly sufferedat low head. At low head, the trajectory taken by a jet of water remainsconstant, even as physical bucket size increases for larger machines.For nozzles with substantial upward tilt angles, a substantialproportion of flow streamlines can re-enter the machine after exit,causing drag losses.

Computational Fluid Dynamics (CFD) studies were performed to quantifythe issue. A novel solution was identified in which head-insensitiveefficiency can be achieved with a certain range of nozzle tilt angles,ideally close to zero° (e.g., providing a horizontal jet). Though thelong axis of the linear system (parallel to axial separation distance144 or pitch line of the powertrain belt) need not be arranged entirelyhorizontally, horizontal implementations are contemplated and useful forthe purposes of discussion herein. Linear turbine systems may benefitfrom slight upward jet tilt (e.g., 5-15°) due to substantial reductionsin the space required, at the expense of more complicated bladecrossbeams, to accommodate the nozzle. In an embodiment, a nozzle may beinclined between 5-20° inwards. This allows placement of the center ofhydraulic pressure of the buckets, near or coincident with the pitchline of the powertrain belt 134, which minimizes operating moments andspan of the crossbeams.

One approach to a head-insensitive efficiency is found in changing thenozzle tilt angle. Testing has shown that the efficiency of relativelylarge buckets is very sensitive to this angle. For nozzles pointedstraight to the side (horizontal) or even slightly downward, theefficiency becomes increasingly head-independent. An added benefit isthat the exit water may take less axial space to clear out of themachine. FIG. 22 illustrates the strong dependence of low headefficiency and normal force vs. nozzle angle. In the simulation plotted,the distance from the nozzle exit to the bucket center is 0.326 m, so at16 degree tilt, the vertical drop is 0.09 m. Lines 2403 a, 2406 a, and2410 a represent efficiency at 3 m, 6 m, and 10 m of head, respectively.Lines 2403 b, 2406 b, and 2410 b represent the ratio F_(n)/F_(t) of aforce normal to the belt back F_(n) to the tangential force F_(t) (theuseful torque-producing force) at 3 m, 6 m, and 10 m of head,respectively. The relative efficiency impact is small at 10 m head butat 3 m head, this drop will account for some about 2.8% of the buckethead. Note the strong dependence of F_(n)/F_(t) on nozzle tilt. For anundershot linear turbine, a slightly positive F_(n)/F_(t) ratio meansthat the jet helps levitate the belt span (supporting belt and blademass). This could be useful to reduce catenary belt deflection. Astrongly negative F_(n)/F_(t) ratio will add tension to the beltattachment bolts, and will induce belt sag reducing clearance betweenthe belt and the nozzle. From these trends and general observations, anozzle tilt angle with respect to horizontal of about +5° is areasonable compromise of head-insensitive efficiency and a F_(n)/F_(t)ratio near 0, while also allowing wider belt spans and less curvycrossbeams than a jet exit angle equal to about 0.

FIG. 20 illustrates nozzle 1022 sloped down at −5°, with accompanyingcrossbeams and buckets, the angle denoted by “0”. FIG. 21 illustrates anozzle tilted up +5°, and buckets' center located coincident with beltback plane. FIG. 20 illustrates how the shape of crossbeams 2038 andnozzle 1022 are configured to match each other. Crossbeams 2038 andnozzle 1022 are shaped to utilize dual sprockets 2036, which are mountedon drive shaft 2028. In some embodiments, a single sprocket may be used.Like previous embodiments of a linear turbine, the single-stage linearturbine of FIG. 20 similarly includes second shaft with set of sprockets(though not shown). First and second plurality of buckets are shown byswept path 2031 and swept path 2031, respectively. Crossbeams 2038 aredesigned to clear nozzle outlets 1027 a, 1027 b so that the buckets arelocated proximal to nozzle outlets 1027 a, 1027 b. In some embodiments,buckets attached on either side of the crossbeams can be housed inindependent bucket covers that can be independently removed formaintenance. As shown in various figures such as FIGS. 20 and 21, thebold “X” marks the center of pressure on the bucket, imparted by the jet(schematic flow lines shown for illustrative purposes). Additionally,“H_(j)” denotes the jet height, and “W_(b)” denotes bucket width, and“L_(j)” denotes jet length. Schematic flow lines are shown forillustrative purposes.

The implementation of downward-tilted, or even horizontal, nozzle, mayinfluence additional design parameters. For example, the crossbeam maybe configured as a recurve-bow shape to clear the nozzle, which isdesigned to occupy minimal space to ensure low losses in turning theflow. The curved crossbeam shape removes space budget within theturbine, making it important to check clearance with various chassisconcepts. Further, the dual sprocket design may allow for a wider spanthan in a single central belt/sprocket design, in that a plurality ofsprockets may distribute the belt over a larger support structure. Thebucket's center of pressure may advantageously be positioned close tothe belt back plane to keep moment loads low.

Nozzle Flow Control System

Embodiments of the linear turbine may include a closure mechanism tocontrol an area of the opening of a nozzle outlet. The linear turbinesystems described herein have particular application to natural sourcesof water, such as rivers. Such sources typically have a significant flowvariability, causing a turbine to need to operate at a wide range offlow rates. A turbine is conventionally optimized to accommodate amaximum predetermined flow from the natural source. When flow from thesource is less than the maximum predetermined flow, the turbine mayexperience a significant loss in efficiency. For example, the efficiencyof propeller-type turbines declines rapidly at any flow rate less thanthe maximum design flow. Conventional high head Pelton turbines, on theother hand, maintain high efficiency across a wide range of flow rates.As shown in FIG. 70, a conventional Pelton turbine has an adjustableflow control mechanism in the form of an adjustable spear 306 withinnozzle 302. Such a conventional solution, however, is not generallyapplicable to the unique linear turbine systems described herein. Forexample, nozzle 122 described herein may have a rectilinear outletopening, from which a free jet uniformly exits at an angle to theopening.

As shown in the partial perspective view of FIG. 24, a first closuremechanism may be, for example, a first slide gate mechanism 2690 a thatmoves from a position adjacent a proximal end of the first substantiallyrectilinear opening toward a distal end of the first substantiallyrectilinear opening to reduce the area of the first substantiallyrectilinear opening 2627 a. A second closure mechanism may also be usedto control an area of the second substantially rectilinear opening. Likethe first closure mechanism, the second closure mechanism may be, forexample, a second slide gate mechanism 2690 b that moves from a positionadjacent a proximal end of the second substantially rectilinear openingtoward a distal end of the second substantially rectilinear opening toreduce the area of the second substantially rectilinear opening.

Slide gate mechanisms 2690 a, 2690 b may be separate modules mounted atoutlets of nozzle 2622 or integrated into nozzle 2622. As shown in FIG.24A, a slide gate 2691 may be vertically mounted with respect elongatedrectilinear opening 2627 a. Such an arrangement allows dual parallelactuation of slide gate mechanisms 2690 a, 2690 b. In an embodiment,rectilinear opening 2627 a and slide gate 2691 may be angled withrespect to vertical. Though in an embodiment slide gate mechanisms 2690a, 2690 b may function independent of one another, linking the slidegate mechanisms 2690 a, 2690 b allows for a reduction in the number ofactuation elements needed. It is also desirable to move both slide gatemechanisms 2690 a, 2690 b at the same time, at the same rate, and in thesame manner. Differences in the size of the openings in nozzle 2622 mayinduce undesirable twisting forces in the turbine. An actuator andlinkage system may be used to simultaneously move first slide gatemechanism 2690 a and second slide gate mechanism 2690 b together.Alternatively, the first closure mechanism may include a rotatablewicket gates positioned adjacent the first substantially rectilinearopening. In either case, first closure mechanism may include anelastomeric seal 2694 and a seal retainer 2695. Seal retainer 2695 mayhave a sharp edge such that the first rectilinear jet of fluid separatescleanly from the seal retainer.

Similar to the above described embodiments, FIG. 23 shows a linearturbine system 2500 with a nozzle 2522 for redirecting flow from around-to-polygonal adapter section 2523 toward buckets connected bycrossbeams 2538 and enclosed by two parallel swept paths, showing thepath of the buckets 2531, 2532. A slide gate assembly 2590 is integratedwith nozzle 2522 (shown with the slide gate retracted). FIG. 24 showsslide gate assemblies, mounted on nozzle 2622, with the slide gatepartially retracted. FIG. 24A shows a cross-section view of one side ofthe system shown in FIG. 24, illustrating details of slide gatemechanism 2690 a including gate guides and seals. A variety of designsare possible to implement the gate and guide system beside the conceptshown. For example, the slide gate guide bearings 2963 may be linearrails rather than slots. In some embodiments, the orientation of theslide gate may be substantially perpendicular to projected jet vector,rather than vertical as shown.

Similar to FIGS. 15 and 16, FIGS. 25-30 illustrate how flow angle andC_(v) changes with respect to flow conditions for nozzle arrangement1122 at different slide gate positions. FIGS. 31-33 illustrate that massaveraged flow angle decreases by roughly 3° when slide gate is not fullyopen, while nozzle losses reduce slightly as flow rate goes down. Thisshould be taken into account when predicting flow rate at part flow, aswell as bucket efficiency. Test results plotted in FIG. 34 shows thatthe turbine maintained high relative efficiency across a wide range offlows, with less than 7% change in hydraulic efficiency from full flow,to 25% of full flow. These values are exemplary in a small model withrelatively higher internal mechanical friction. Larger commercial-scaleturbines will have relatively lower mechanical friction versus thehydraulic power being produced.

FIG. 35 is a plot of efficiency vs. the ratio of jet height to bucketwidth.

FIG. 36 is a plot of efficiency vs. Q/Q*.

FIG. 37 is a plot of efficiency vs. jet angle.

In an embodiment, slide gate 2691 may be made solid, without anyfolding. A rack and pinion, for example, may be used for actuation.Because the rack may be difficult to seal at the vacuum housinginterface, a protective housing may be fitted over the gate in itsextended position. This housing is configured to avoid problems withicing. The rack actuator may be housed in air and drive the pinion viaan extension shaft. The length of the penstock/inlet-to-distributoradapter 2523 is such that the sliding gate can be accommodated without alarge additional length penalty, so a rigid, non-folding gate may be afeasible option for many sites. This provides valuable flexibility,particularly for high head sites where the loads required for fullclosure and opening may be quite large for a coiling design.

In an alternative embodiment, a coiling gate is used for compactpowerhouses to reduce the overall length of the turbine. Feasibility ofcoiling the gate depends to some extent on the design criteria such asmaximum allowable panel deflection, and max allowable bending stressduring the coiling operation (which defines the max allowable bendradius). The following list provides other, non-limiting exampleembodiments of the slide gate: a simple spooled sheet metal; plates onroller chain; rigid pinned sections; sheet metal with reinforcementbars; bars and a pretensioned cable framing a rubber seal sheet; barswith a cable attached to each bar and a sealing mechanism; and bars witha sheet acting as a living hinge. Drive options include, but are notlimited to: holes in sheet metal and plates; rack gears on inside faceof plates; and a gear rack on the outside edge of a plurality of plates.

In further aspects, flow control can be achieved by using one butterflyvalve on each distributor, using slide gates, and/or using segmentedslide gates. Segmented hinged panels or wicket gates may also be used asan alternative to a slide gate.

Bucket Shape

With reference back to FIGS. 1-5, nozzle 1022 directs a free jet at anangle α₁ to direction of bucket travel 1040. The shape of the bucket isconfigured such that the flow a free jet is redirected in a directionopposite to the direction of travel 1040 and away from the turbine at anangle β₂. These parameters play an important role in determining theamount of work done by the linear turbine and hence its efficiency.

FIGS. 38, 39, and 40 show an exemplary bucket design for a linearturbine, with FIGS. 39 and 40 illustrating a partial cascade ofexemplary buckets, their dimensional relationship, illustration ofsolidity, and fluid illustration from a CFD simulation showing the pathof fluid once it impinges upon a bucket as it moves.

FIGS. 38-45 a/b illustrate a bucket design that is specifically designedfor a linear turbine (e.g., linear Pelton turbine). Buckets of asingle-stage linear turbine may be designed to enable all orsubstantially all streamlines to exit across the blade, withsubstantially no re-entrant streamlines. The bucket 4010 show in theseFIGS. enables efficient clearing of water around perimeter of bucket,with no or substantially no re-entrant streamlines (see FIGS. 39 and40); virtually shockless entry; a defined separation point around bucketlip; a defined separation point on bucket backside (creating anintentional air cavity in which the crossbeam and associatedbucket-mounting hardware can fit without any drag or back splashing); arounded leading edge (enabling parametric design for various goals, suchas high efficiency or fish passage); an integrated rib (providing alocation for threaded fasteners with minimal negative impact onefficiency); and a bucket shape that may be configured to be elongatedor reduced in embodiments with varying jet width jets.

While previous buckets displayed flow that for the most part exited thebucket to the side and downward, a noticeable amount of flow visiblyexited the upper perimeter of the buckets and re-entered the turbineinterior. This flow created a drag force as subsequent blades impelledthe fluid. Ultimately some of this trapped flow is flung out of themachine as the blades turn around the distal sprocket, emerging as alarge “roostertail.” To reduce roostertailing, in some embodiments, thenozzle/jet may be positioned further from the return axle. Further, insome embodiments linear travel may be increased so that the fluid mayfully exit the bucket prior to returning.

Bucket 4010 is self-centering, that is, it balances itself along adirection of travel (such as a plane defined by the belt). Becausebucket 4010 has concave curvature on either side of the incoming jet,there will be a restoring force which rises in magnitude in proportionwith the degree of parallel misalignment to the jet.

A front concave surface of bucket 4010 is formed by parametriccurvature-smooth blends (conics), allowing tuning of the bucket's shapeto eliminate problems such as backsplashing, while maximizing the amountof flow turning (efficiency). FIG. 40 shows how the bucket's slopevaries. The side and tips have tight curvature (approximately 8° and 9°respectively) while the corner area has lower slope (approximately 27°)to allow the flow in that area to exit at an angle large enough to clearthe blade.

FIGS. 41-45 b, for example, shows a concave surface extending to meetthe jet inlet with an angle that minimizes shock or sudden change influid angle. A rounded leading edge, the radius of which can vary, isuseful for improving safety of biological organisms, such as fish, whichmay pass through the turbine (e.g., “fish-friendliness”). A rib 4012 inthe concave bucket surface allows a local thickness increase andprovides room for a threaded hole 4016 allowing use of fasteners toattach the bucket to the blade beam. The rib is smoothly blended intothe surrounding bucket. Curvature extends fully around the perimeter ofthe bucket. A clearly defined separation edge 4020 around the bucket rimallows the water to cleanly exit the bucket. The rim face may beapproximately perpendicular to the surface. A clearly defined separationedge on the bucket convex backside that resembles a ramp or wedge 4014terminates in a sharp edge, forcing the jet to cleanly split off theramp in a deterministic way. A flat pad area 4018 provides a stableattachment surface for the crossbeam tab. A rim whose shape allowssubsequent buckets to clear each other without colliding, particularlyas they travel around the sprockets. As shown, the angle of the surfacewith respect to the bucket travel vector is plotted with contour lines.

The bucket 4010 show a significant improvement versus bucket 4310. Themachine with buckets 4010 was tested to be about 84% efficient, vs.about 71% for the machine with buckets 4310. In some tests, the measuredturbine efficiency peaked at a lower than expected value of U/Vjet, inpart because the nozzle design had not yet been optimized. For example,visible flow was still being entrained in the machine, and being flungup in the air by returning buckets.

FIGS. 41 and 42 show the interaction of fluid with the buckets, showingthe air gap on the back side of the buckets. In this regard, the airpocket allows for space to fit the cross-beams, other mechanicals, andallows for clearance and lack of backsplashing/interference with thecascade of buckets as the buckets move along their path. The air pocketallows for the tabs of the cross beam to couple to the bucket. As shown,it shows substantially no sideloading. These figures also illustrate thetheoretical nature of FIG. 5. While the jet enters the bucket at acoherent vector, it immediately begins to spread out along the surfaceof the bucket as it is deflected by the bucket surface.

These results show that performance of the entire machine is based on acombination of buckets and nozzle, rather than just buckets alone. Basedon observation of flows during the tests, it is apparent that remainingundesirable dynamics may be improved upon. These dynamics may be due toan interaction of sub-optimal, non-uniform streamlines exiting thenozzle, with the blades. For example, it was observed that returningbuckets may fling water up in the air (known as a rooster tail). Thismeans that jet flow is not completely clearing across the bucket beforethe buckets are forced to return around the axle. Some fluid remains ina bucket which flung upward when the bucket reaches an arc-shapedsegment of the travel path. Repositioning or retracting the nozzle endmay allow additional linear travel so that water can fully exit thebucket prior to returning. It was also observed that buckets proximal tothe fluid inlet cleared water to the sides more effectively than thebuckets in the mid-span. This behavior was attributable to non-uniformstreamlines exiting the nozzle. This issue may also be addressed byoptimal nozzle design.

Bucket 4310 is shown, for example, in FIGS. 43-47 a/b. Each of thebuckets 4310 can have a dimension C and a width W. Dimension C may be ina range from approximately 90 mm to approximately 115 mm, such as in arange from approximately 100 mm to approximately 105 mm. Width W may bein a range from approximately 110 mm to approximately 130 mm, such as ina range from approximately 115 mm to approximately 120 mm. As shown,bucket may also include dimension L, shown as a linear distance of theedge of the bucket along its width, prior to the curvature of thesidewalls of the bucket. This is best shown in FIG. 47a . Dimension Lmay be varied while curvature remains constant, allowing for a widerplatform for jet impingement.

Each bucket may be removably mounted to an end of a crossbeam throughattachment holes. A first attachment hole can be spaced from the top ofbucket 4310 a distance D1. In an embodiment, D1 be in a range fromapproximately 40 mm to approximately 50 mm. A second attachment hole canbe spaced from the first attachment hole a distance D2. In anembodiment, D2 be in a range from approximately 5 mm to approximately 20mm. Bucket 4310 can have a depth Z. In an aspect, Z be in a range fromapproximately 25 mm to approximately 35 mm.

A top portion of bucket 4310 may have an angle β_(2a) from a rearportion of bucket 4310. In an embodiment, β_(2a) can range fromapproximately 5° to approximately 15°. In an embodiment, β_(2a) canrange from approximately 0° to approximately 20°. A bottom portion ofbucket 4310 can have an angle β_(2b) from a rear portion of bucket 400.In an embodiment, β_(2b) may be in a range from approximately 5° toapproximately 15°. In an embodiment, β_(2b) may be in a range fromapproximately 0° to approximately 20°. These angles are tuned such thatthe efficiency may be increased, and so that the buckets do not hit eachother, particularly when the buckets enter or exit the curved paths.

Similar to a conventional Pelton bucket, a front surface of bucket 4310may include concave surfaces. The concave surfaces may have a radius ofcurvature ranging from approximately 25 mm to approximately 35 mm. Insome embodiments the concave surfaces may have a constant radius ofcurvature. In other embodiments, the concave surfaces may have a varyingradius of curvature. Bucket 4310 may have a thickness T. In anembodiment, T may be in a range from approximately 1 mm to approximately5 mm, such as in a range from approximately 2 mm to approximately 4 mm.

The dimensions referenced herein are exemplary, and are non-limiting.The dimensional ranges may be scaled, for example, to be utilized in alinear turbine system of a larger scale, such as a turbine of up to orexceeding 1 megawatt.

Crossbeams

The linear turbine systems described herein may utilize cantileveredcrossbeams that are mounted to a belt of the linear turbine. Thecrossbeams may be a part of a turbine blade. The buckets may be attachedto the crossbeams (e.g., of the turbine blade). The crossbeams areconfigured to be centered mounted and configured to carry a bucket ateach end. The cantilevered crossbeam design enables identical buckets tobe used on the left side and right sides of the crossbeam. Thecrossbeams are configured to be placed in the linear turbine so as toavoid interference with water. Crossbeam 4870 is shown, for example, inFIGS. 46-49. Crossbeam 4870 includes a flat central mounting portion4871 for mounting crossbeam 4870 to a belt or similar structure of alinear turbine. The crossbeam attachments may be centered at the centerof mass to minimize inertial moments as the blade assembly moves aroundthe shaft axis. Two symmetrical cantilevered arms 4872 extend fromcentral mounting portion 4781. As shown in the figures, cantileveredarms 4872 may be sized and shaped so as to accommodate sprockets of thelinear turbine, clear a nozzle, and properly position buckets at anozzle outlet. Bucket mounting portions 4873 are integrally formed ateach distal end of cantilevered arms 4872. Bucket mounting portions 4873include through-holes 4874 that are configured to accept fasteners intothrough-holes 4874 for attaching a bucket to crossbeam 4870 at each end.In other embodiments, the buckets and crossbeams may be integrallyformed, or fastened in other suitable ways, such as welding. In someembodiments, buckets and crossbeams together make up the turbine blade.Central mounting portion 4781 may include interlocking finger extensionsto provide an increased moment arm to resist hydraulic moments. Thecrossbeam 4870 may be made, for example, from aluminum, an aluminumalloy, stainless steel, or a fiber-reinforced composite such as carbonfiber or fiberglass in an epoxy or thermoplastic matrix.

The bucket and crossbeam assembly is shown, which may make up a turbineblade, for example, in FIGS. 50-54. Because of the shape of crossbeam4870 and the position of bucket 4310 on crossbeam 4870, the buckets 4310can be hydraulically self-centering. This assembly may comprise aturbine blade, as used herein. A turbine blade may include one or moreof these components. Fasteners are shown, which may connect crossbeam4870 to the belt/chain; and also bucket 4010 to crossbeam 4870.

The crossbeams may be attached directly to a belt, e.g., requiring nobearings or parts having sliding relative motion.

Each side of buckets attached to the crossbeams can be housed in anindependent cover that can be independently removed for maintenance. Alinear housing central housing can support the nozzle. The shaftattached to the belt sprockets can turn on bearings attached to a commonbaseplate.

Mechanical Arrangement

U.S. provisional patent application 62/367,003 discussed using shaftswhose bearings were located far outboard of the runner. A length anddiameter of the shafts may be reduced by utilizing a chassis in whichthe bearings are brought inward and are located in close proximity tothe powertrain sprockets.

FIG. 55 illustrates an over-head cross-sectional view of a compactmechanical arrangement. Conventional industrial roller bearings 5739 aremounted in pillow block housings affixed to a single plate 5764. Plate5764 having all bearing locations machined in the same operation issecured to plinth 5760. In some embodiments, plinth 5760 may coact withother elements of the system to provide the draft chamber and relativevacuum features described herein. Axle bearings may be added at any of 4locations to accommodate left-hand or right-hand overhung loads, etc.Widely spaced belts and sprockets 5736 add torsional stability and mayallow elimination or deprecation of any powertrain guide rails. Withthis arrangement, belt attachments may be simple bolts without movingparts. As an additional benefit, a mass of each sprocket 5736 is halved,and the manufacturing process to produce them (such as castings) may besimpler, with less expensive tooling. The chassis design comprises astructure that is simple yet allows repeatable positioning of theoutboard bearing in this configuration. These configurations mayincrease the stiffness of the system and decrease the free span.According to site installation requirements, the blades and belt may betuned to avoid natural frequencies leading to unfavorable resonance.

The compact linear turbine system 5700 shown in FIG. 55 may include manyof the features described herein with respect to other embodiments. Forexample, linear turbine system 5700 may include a slide gate mechanism5790, which operates in a similar manner to slide gate mechanism 2690 adescribed with respect to FIGS. 26 and 26A. Linear turbine system 5700may also include bucket swept paths, showing the paths of the buckets5731, 5732, which function in a similar manner to paths 2531, 2532.Linear turbine system 5700 may further include a round-to-polygonaladapter section configured to direct fluid flow from a penstock to anozzle inlet in a manner similar to round-to-polygonal adapter section1123, described with respect to FIG. 12. Linear turbine system 5700 maybe configured to drive an electric generator in a manner similar to thearrangement illustrated by FIG. 1. Linear turbine system 5700 may alsoutilize a powertrain tension control system, such as take-up mechanism5765. Powertrain tension control is further described below.

Powertrain Tension Control

Powertrain tension control is used in a linear turbine to maintainproper tension even as perturbations such as ambient temperature changesor ingestion of foreign objects occur. A spring loaded take-up may bedesigned to accomplish passive tension control without additionalcomplex systems (as would be required by hydraulic or pneumatictake-ups). FIG. 56 illustrates a take-up mechanism 5865 utilizing aspring (such as a set of Belleville washers, for example) that ispressed using a stainless screw jack. Take-up mechanism 5865 may be inline with a belt center of load.

The powertrain may include additional mechanical components, such as aflywheel configured to provide useful inertia. In some embodiments, theflywheel may be replaced with or augmented by a shaft brake. Highproportionality of nozzle control eliminates need for large inertiaduring startup. Shaft brake can be timed to come on only if turbineexceeds a particular speed limit while nozzle is attempting closure(i.e., if nozzle can close quickly enough, then brake will not trip on).

Tailwater Suction without Submergence

Linear turbines as described above may operate in an air-filled vacuumcase, in which air bubbles are entrained by the jet and evacuated fromthe case by momentum of the outgoing fluid. As these bubbles areevacuated, the lower pool is sucked upwards in the draft chamber,recovering useful head below the turbine. This concept allows theturbine and associated equipment to be situated above tailwater, yet notlose the water fall below the turbine as working head. This is useful,for example, to avoid damage from flood waters, accommodate naturalvariations in tailwater, and to minimize construction cost.

FIG. 57 illustrates a linear turbine, such as linear turbine 100, in thecontext of a site having a difference in elevation 5914 between a poolof working fluid, such as water, at an upper elevation 5905 and a poolat a lower elevation 5906. The fluid is conveyed through an intakeconduit or penstock 5921 into a nozzle 122, which is disposed withinhousing or enclosure 5932. In this regard, the nozzle and housing may becoupled together such that a relative vacuum compared to the ambientatmosphere may develop. This enclosure extends below the surface of thelower pool, such that an enclosed atmosphere is isolated from theambient external atmosphere. The length of the penstock 5921 or inletcan be arbitrarily large as needed, and its shape can be any convenientshape, such as circular or rectangular in cross-section.

The working fluid, such as water, moves under pressure through a nozzle122 and exits the nozzle as a free jet. The system shown in derivespressure due to a difference in water levels of two pools, but in otherapplications, this pressure can come from any available source, internalwater level 1000 is shown for illustrative purposes, and may varyrelative to system operation and operating conditions. The linearturbine shown may operate in a manner as described with linear turbine100 described with respect to FIGS. 1-4.

As the free jet of working fluid engages blades 130 of the turbine, airfrom the enclosed atmosphere is entrained in the working fluid andcarried with the outlet flow in the form of bubbles 5907. Upon exitingthe system into the lower pool, bubbles 5908 rise to the surface andrejoin the external atmosphere. Because the housing 5932 is airtight,the evacuation of air from the internal atmosphere will create a vacuumpressure, which elevates the internal water level within the housing toa distance 5909 above the external lower pool elevation 5906. An airinlet valve 5911 is provided to enable replenishment of fresh air fromthe external atmosphere, into the internal atmosphere.

This valve can be regulated such that a desired vacuum pressure ismaintained inside the enclosed volume. The vacuum pressure adds to theusable pressure on the linear turbine, allowing the turbine to use mostof the available elevation difference 5914, while also allowing theturbine to be placed at a convenient elevation above the lower pool,such as to avoid damage during high flow events, such as floods. Thiscapability is important at hydropower projects that have small elevationdrops, since the proportion of the total available drop represented bythe unit elevation above tailwater can be significant. For example, at aproject with 6 meters of total drop from upper pool to lower pool, theunit may need to be positioned 2 meters above the lower pool, so as toavoid being damaged when the tailwater rises during floods. The abilityto use vacuum suction allows the turbine to take advantage of the 2meters of drop that would otherwise be lost.

Rapid Depower

Hydropower plants must be designed to operate safely even if the utilitygrid connection is lost. Normally, in the event of power loss, theturbines must be quickly shut down to prevent risk of damage due to highspeed operation. Conventional high-flow turbines, such as Kaplan, bulb,circular crossflow, and Francis turbines, are subject to large pressurefluctuations (known as water hammer) if the turbine is suddenly turnedoff or if a grid-disconnect event occurs and the machine rapidlyaccelerates. Water hammer occurs when all the water flowing throughthese types of turbines is suddenly stopped to fully depower theturbine. Conventional Pelton turbines, used only at sites having veryhigh pressure, benefit by being able to use a jet deflector plate todivert the water stream/jet in an emergency, which allows fast and safeshut-down without water hammer, because only the direction of flow ischanged, not the rate of flow. The U.S. provisional patent application62/367,003 discussed ways of rapid depower, including jet deflector,deflector jets, and a relief valve.

Alternative means of rapid depower are herein disclosed, includingmethods of rapidly “swamping” the buckets, causing fast degradation ofefficiency at overspeed conditions. As used herein, “swamping” denotes asystem that causes fluid that exits one of the plurality of buckets intoa rear surface of an adjacent bucket. A “swamper” may include portionsof a system that effect this, including a deflector/pivot plate. In anembodiment, a linear turbine system may include a depower systemconfigured to cause rapid degradation of efficiency of the turbinesystem at an overspeed condition. The depower system may include adeflector with the deflector arranged to selectively divert a portion ofthe fluid jet away from a plurality of buckets, such as buckets 110,120. The deflector may include a pivot plate. The pivot plate may bearranged between the nozzle and the plurality of buckets. In anotherembodiment, the depower system may include a deflector arranged exteriorto the plurality of buckets to direct fluid that exits one of theplurality of buckets into a rear surface of an adjacent bucket. Thelinear turbine system may further include a control system to controlthe depower system in increments.

The linear turbine theory discussed above shows that runaway speedmultiple is a function of the jet angle. For example, at a 33 degree jetangle α, the no-load speed ratio is U/Vu=2.23, compared to the optimalefficiency speed ratio of U/Vu=0.69. Ignoring windage or drag, thisyields a 3.23× speed increase. The actual multiple will be smaller thanthis value due to nonlinear increases in drag and bucket splashing, butwe need to carefully consider increasing the speedup spec for allrelevant components (belt attachments, bearings, generator etc.).Real-world conditions will involve fluid-dynamic drag at faster thanoptimal speed as well as mechanical friction and windage, all of whichwill reduce efficiency more quickly than the ideal theory, keeping theoverspeed multiple to about 2.25×.

Various jet deflector shapes are possible. In one embodiment, a partialdeflection may reduce overspeed multiple yet not actually completelystarve the bucket immediately. This allows a much smaller and simplerdeflector mechanism when compared to a solution which completely divertsthe jet. For example, a small pivoted plate may be used for partialdeflection, instead of a large plate on a 4-bar linkage. In anembodiment, a small pivoted plate may be configured to reduce theoverspeed multiple from 2.25× to 1.8×. This condition will result inmoment loading of the bucket relative to the belt, but this load willdissipate quickly as the unit runs up to the speed-no-load condition.

In an alternative embodiment, a plate may be arranged outboard of aplurality of buckets (opposite the nozzle) to interfere with flowotherwise exiting the turbine. A nozzle and bucket arrangement of alinear turbine system may be designed to efficiently redirect a fluidflow as shown in FIG. 4. A plate may be pivoted, translated, orotherwise positioned proximal to a plurality of buckets on a sideopposite a nozzle. By blocking the flow of fluid, fluid remainsentrained in the turbine naturally impeding the travel of the buckets.FIG. 58c illustrates how the system acts as a “swamper” to rapidly causedrag loads on the buckets.

FIG. 58a shows a baseline embodiment, having no deflector. As shown, gap“G” between the nozzle 122 and the bucket 110 (attached to crossbeam138) is shown. This allows travel within the system, as well as room toposition other mechanical systems within the space (such as flow controlmechanisms and rapid depower mechanisms). The distance of this gapaffects structural rigidity of the system, e.g., the turbine bladeincluding the cross beam and bucket, so that as the distance increases,other dimensions may be required to be altered, including those of thecomponents of the turbine blade, belt, and powertrain generally. FIG.58b shows a Jet deflector 6010, which may be used to direct a portion offluid that has exited the jet away from the bucket. In this regard,better control of the flow impinging on the buckets can be achieved,without a large pressure load (for example, if the flow was cutoff atthe nozzle exit itself, sealing the opening). FIG. 58c shows the swampersystem, where fluid that has exited the buckets is directed back towardsthe backside of the buckets by swamper 6012. FIG. 58d shows a deflectorjet 6014, which may include holes 6014 drilled at an angle in a plate.The holes may direct fluid exiting the nozzle at a given angle to adifferent angle, e.g., at an angle coming out from the page, asillustrated. This will also direct fluid to the backs of the buckets. Insome embodiments, the deflector jet may be a series of nozzles, that mayhave an adjustable angle. In these embodiments, fluid may be directedtowards either the front or back of the buckets. Each of the fluidaltering systems may be used to slow or stop the turbine, and each maybe adjustable such that a rate of slowing or stopping may be controlled.

Further Embodiments

FIGS. 59-61 illustrate a linear turbine system with a dual distributionarrangement. A dual distribution system may be utilized to takeadvantage of the symmetry of a linear turbine system. Penstock 6121utilizes a Y-junction 6180 to feed flow 6124 to an upper nozzle 6122 aand a lower nozzle 6122 b. Upper nozzle 6122 a and lower nozzle 6122 beach provide a free jet impulse to both of a first plurality of buckets6110 and a second plurality of buckets 6120. Upper nozzle 6122 and lowernozzle 6122 b are arranged in opposite directions so as to provideimpulse power in opposing directions to the corresponding linearsegments of first plurality of buckets 6110 and second plurality ofbuckets 6120. The resultant forces combine to increase the collectiveforce on the turbine. Just as with previously described embodiments, thebuckets are mounted on crossbeams 6138 and transfer the impulse power tobelt 6134. Forces on belt 6134 turns sprockets 6136, as well as firstshaft 6128 and second shaft 6129, which may be used, for example, forelectric power generation. Respective bearings 6139 may carry firstshaft 6128 and second shaft 6129. Bearings 6139 may be outboard of thebucket assemblies as shown in FIG. 59. Alternative, bearings 6139 may bearranged similar to the arrangement shown in FIG. 55. In an embodiment,first plurality of buckets 6110 and second plurality of buckets 6120 maybe disposed within a housing such as enclosure 6131. Enclosure 6131 maybe part of a larger general linear turbine housing, for example. Firstshutoff valve 6181 and second shutoff valve 6182, which may be, e.g.,butterfly valves, may utilized to independently adjust the amount offlow to either upper nozzle 6122 a or lower nozzle 6122 b.

FIG. 62 shows a linear turbine system having a split-chassisconfiguration, in that the shaft 6228 and generator 6229 may be doubledand split relative to the direction of crossbeam 6238.

FIG. 63 shows a linear turbine system having a roller bearing system,where one or more sprockets 6336 is disposed generally centrally to thelinear direction of the linear turbine.

FIG. 64 illustrates a linear turbine system 6600 according to anembodiment. This embodiment differs significantly from previousembodiments. Linear turbine system 6600 includes Pelton-type blades 6685that are mounted directly to a belt 6634. Also, instead of providing afree jet at a non-zero angle α as with previous embodiment, a free jetis parallel to path of travel of blades 6685 (α=0). In this aspect,linear turbine system 6600 operates similar to a convention Peltonturbine as described with respect to FIG. 73. To make use of the linearnature of linear turbine system 6600, however, the rectilinear free jetangled with respect to a linear segment of the linear turbine as shown.Linear turbine system 6600 otherwise operates similar to the otherembodiments described. A nozzle may be configured to form a rectilinearfree jet incident on more than two blades 6685. Belt 6634 is arrangedabout sprockets 6636. Sprockets rotate about parallel shafts 6628, 6629.

FIGS. 65-66 illustrates a linear turbine system 6700 utilizingvariations of an inward-flow concept. Linear turbine system 6700 issimilar to previously described outward-flow embodiments, but isconfigured to direct two rectilinear free jets toward a center axis ofthe turbine. Similar to the embodiment shown in FIGS. 1-4, a firstplurality of buckets 6710 and second plurality of buckets 6711 may bemechanically linked so as to rotate together on first shaft 6728 secondshaft 6729 respectively about first axis 6712 and second axis 6713.Linkages may be in the form of dually cantilevered crossbeams 6738,which couple one individual bucket from each of first plurality ofbuckets 6710 and second plurality of buckets 6711 by fixedly mounting abucket on either end of the crossbeams 6738. Crossbeams 6738 are centermounted to a powertrain that is configured to constrain the crossbeamand bucket assemblies along endless continuous path. The buckets maytravel along linear segments between parallel shafts 6728, 6729. Aforked nozzle 6788 directs fluid flow 6724 from a penstock 6621 outboardof the turbine buckets and provides a rectilinear free jet impulse tofirst and second plurality of buckets 6710, 6711 at an angle α withrespect to a plane that extends along a substantially rectilinearopening of forked nozzle 6788. Forked nozzle 6788 may include guidevanes or wicket gates 6789 (see FIG. 67) to assist in inducing thedesired jet angle. Forked nozzle 6788 may be mounted underneath theturbine chassis. A separation of first and second plurality of buckets6710, 6711 may be sufficient that fluid flow from each side of theturbine does not significantly interfere with jet exit from either sidesuch that it lowers efficiency of the turbine.

As shown in FIG. 66, nozzles may be configured in opposite directionsalong the linear direction (including nozzles 1621, outlets 1623 a/b,and parallel shafts 1628 a/b).

The Summary and Abstract sections may set forth one or more but not allexemplary embodiments of the present invention as contemplated by theinventor(s), and thus, are not intended to limit the present inventionand the appended claims in any way.

The foregoing description of the specific embodiments will so fullyreveal the general nature of the invention that others can, by applyingknowledge within the skill of the art, readily modify and/or adapt forvarious applications such specific embodiments, without undueexperimentation, without departing from the general concept of thepresent invention.

Features of each embodiment disclosed may be used in each of the otherembodiments disclosed.

Therefore, such adaptations and modifications are intended to be withinthe meaning and range of equivalents of the disclosed embodiments, basedon the teaching and guidance presented herein. It is to be understoodthat the phraseology or terminology herein is for the purpose ofdescription and not of limitation, such that the terminology orphraseology of the present specification is to be interpreted by theskilled artisan in light of the teachings and guidance.

The breadth and scope of the present invention should not be limited byany of the above-described exemplary embodiments, but should be definedonly in accordance with the following claims and their equivalents.

What is claimed is:
 1. A linear turbine system, the linear turbinesystem comprising: a linear turbine; and a nozzle configured to providea fluid jet to the turbine, the nozzle comprising: an inlet portion forreceiving a volume of fluid, the inlet portion having a cross-section; afirst outlet portion terminating in a first substantially rectilinearopening to direct a first rectilinear jet of fluid outward to contactthe linear turbine; a second outlet portion terminating in a secondsubstantially rectilinear opening to direct a second rectilinear jet offluid outward to contact the linear turbine; and a bifurcationpositioned between the inlet portion and the first and second outletportions to divide the volume of fluid into the first outlet portion andthe second outlet portion, wherein the first outlet portion directs thefirst rectilinear jet of fluid into the linear turbine at an angleranging from approximately 25° to approximately 50°.
 2. A linear turbinesystem, the linear turbine system comprising: a single-stage linearturbine; a free jet nozzle to supply a fluid jet to the turbine; and ahousing configured to isolate the linear turbine and nozzle from anexternal atmosphere, the housing comprising: a chamber enclosing thelinear turbine and nozzle, the chamber having an outlet that ishydraulically sealed to an outlet fluid body, after the fluid jetcontacts the turbine, fluid leaving the turbine exits the housingthrough the outlet, and a control valve configured to control an amountof air in the chamber to maintain a desired elevation of suction headinside the chamber without allowing the outlet fluid body to contact theturbine.
 3. The turbine system of claim 2, further comprising: a driveshaft driven by the linear turbine, the drive shaft extending throughthe housing and configured to drive an electric generator positionedexterior to the housing.
 4. The turbine system of claim 2, wherein airfrom the enclosed atmosphere is entrained in the form of bubbles andmomentum of the outflow evacuates the entrained bubbles of the enclosedatmosphere from the chamber.
 5. The turbine system of claim 2, whereinthe control valve is configured to automatically maintain a level of afluid pool below the turbine.
 6. The turbine system of claim 2, whereinthe control valve is configured to automatically maintain a pressureinside the chamber below the external atmospheric pressure so as toincrease a level of a fluid pool below the turbine.
 7. The turbinesystem of claim 2, wherein the nozzle receives a fluid source at anozzle inlet, a bottom portion of the nozzle inlet being positioned at afirst elevation, wherein the nozzle delivers the fluid jet to theturbine at a second elevation such that the first elevation is lowerthan the second elevation.
 8. The turbine system of claim 7, wherein thefluid jet exits the turbine at a third elevation and falls to a fluidpool inside the chamber, a level of the fluid pool being at a fourthelevation such that the third elevation is higher than the fourthelevation.
 9. The turbine system of claim 8, wherein an exterior fluidsurrounding the chamber outlet outside the chamber has a level at afifth elevation such that the fourth elevation is higher than the fifthelevation.
 10. The turbine system of claim 2, the linear turbinecomprising: a first shaft extending along a first horizontal axis; asecond shaft extending along a second horizontal axis, the second axisbeing separated from and substantially parallel to the first horizontalaxis; and a first bucket to travel a first continuous path around thefirst shaft and the second shaft along a first plane, the first pathincluding a first substantially linear path segment between the firstaxis and the second axis, a first substantially arc-shaped segmentaround the second axis, a second substantially linear path segmentbetween the second axis and the first axis, and a second substantiallyarc-shaped segment around the first axis, wherein the nozzle isconfigured to direct the fluid jet to contact the first bucket in thefirst substantially linear path segment such that the fluid jet does notcontact the first bucket in the second substantially linear pathsegment.
 11. The turbine system of claim 10, wherein the secondsubstantially linear path segment is positioned above the firstsubstantially linear path segment.
 12. The turbine system of claim 10,further comprising: a second bucket to travel a second continuous patharound the first shaft and the second shaft along a second plane, thesecond path including a first substantially linear path segment betweenthe first axis and the second axis, a first substantially arc-shapedsegment around the second axis, a second substantially linear pathsegment between the second axis and the first axis, and a secondsubstantially arc-shaped segment around the first axis, wherein thenozzle is configured to direct the fluid jet to contact the secondbucket in the first substantially linear path segment of the second pathsuch that the second fluid jet does not contact the second bucket in thesecond substantially linear path segment of the second path.
 13. Theturbine system of claim 10, further comprising: a turbine bladecomprising the first and second buckets, the first bucket beingconnected to a first end of the turbine blade and the second bucketbeing connected to a second end of the turbine blade.
 14. The turbinesystem of claim 13, wherein the first bucket and the second bucket arehydraulically self-centering.
 15. The turbine system of claim 13,further comprising: a moving structure, the turbine blade beingconnected to the moving structure.
 16. The turbine system of claim 15,wherein the turbine blade is connected to the moving structure at itsmid-span such that the first end of the turbine blade and the second endof the turbine blade are cantilevered.
 17. The turbine system of claim15, wherein the moving structure is a belt.
 18. The turbine system ofclaim 10, wherein the nozzle is positioned below a horizontal planeextending between the first axis and the second axis.
 19. The turbinesystem of claim 10, wherein the nozzle directs the fluid jet outward tocontact the first bucket and the second bucket.
 20. The turbine systemof claim 19, wherein the nozzle directs the fluid jet outward to contactthe first bucket at an angle with respect to the first substantiallylinear path segment, the angle having a range from approximately 25° toapproximately 50°.
 21. The turbine system of claim 10, wherein a speedof the fluid jet is greater than a speed of the bucket.